In how many ways can a president, vice president, and secretary be chosen from a class of 20 girls and 30 boys if the president must be a girl and the vice president a boy?

Answers

Answer 1

Given:

Number of girls = 20

Number of boys = 30

The president must be a girl and the vice president a boy

To find:

Number of ways to choose a president, vice president, and secretary.

Solution:

The president must be a girl and the vice president a boy. So, out of three students 1 is girl and 1 is boy. Third student can be a girl or a boy.

Total number of ways = Selecting 2 boys and 1 girl +  Selecting 1 boy and 2 girls

[tex]=^{30}C_2\times ^{20}C_1+^{30}C_1\times ^{20}C_2[/tex]

[tex]=\dfrac{30!}{2!(30-2)!}\times \dfrac{20!}{1!(20-1)!}+\dfrac{30!}{1!(30-1)!}\times \dfrac{20!}{2!(20-2)!}[/tex]

[tex]=\dfrac{30\times 29\times 28!}{2\times 1\times 28!}\times \dfrac{20\times 19!}{19!}+\dfrac{30\times 29!}{29!}\times \dfrac{20\times 19\times 18!}{2\times 1\times 18!}[/tex]

[tex]=\dfrac{30\times 29}{2}\times 20+20\times \dfrac{20\times 19}{2}[/tex]

[tex]=8700+3800[/tex]

[tex]=12500[/tex]

Therefore, the required number of ways is 12500.


Related Questions

si la pendiente es negativa, la linea no es recta?​

Answers

En matemáticas, la pendiente de una línea ( m ) se describe cómo rápidamente o lentamente cambiar se está produciendo y en qué dirección, ya sea positiva o negativa. Funciones-aquellos lineales cuya gráfica es una línea recta-tienen cuatro posibles tipos de pendiente: positivos , negativos, cero , e indefinido. Una función con una pendiente positiva está representada por una línea que sube de izquierda a derecha, mientras que una función con una pendiente negativa se representa por una línea que va hacia abajo de izquierda a derecha. Una función con pendiente cero está representado por una línea horizontal, y una función con una pendiente indefinida está representada por una línea vertical.

La pendiente se expresa normalmente como un valor absoluto. Un valor positivo indica una pendiente positiva, mientras que un valor negativo indica una pendiente negativa. En la función y = 3 x , por ejemplo, la pendiente es positiva 3, el coeficiente de x .

En estadística, un gráfico con una pendiente negativa representa una correlación negativa entre dos variables. Esto significa que como una variable aumenta, la otra disminuye, y viceversa. Correlación negativo representa una relación significativa entre las variables x e y , que, dependiendo de lo que son el modelado, puede entenderse como entrada y salida , o causa y efecto .

¿Cómo encontrar la pendiente

pendiente negativa se calcula igual que cualquier otro tipo de pendiente. Lo puede encontrar dividiendo la subida de dos puntos (la diferencia a lo largo del eje y vertical u) por la carrera (la diferencia a lo largo del eje x). Sólo recuerda que la “subida” es en realidad una caída, por lo que el número resultante será negativo.

m = (y2 - y1) / (x2 - x1)

Una vez que se representa gráficamente la línea, verá que la pendiente es negativa porque la línea bajará de izquierda a derecha. Incluso sin dibujar un gráfico, usted será capaz de ver que la pendiente es negativa, simplemente calculando m utilizando los valores dados para los dos puntos.

Por ejemplo, la pendiente de una línea que contiene los dos puntos (2, -1) y (1,1) es:

m = [1 - (-1)] / (1 - 2)

m = (1 + 1) / -1

m = 2 / -1

m = -2

Una pendiente de -2 significa que por cada cambio positivo en x , habrá el doble de cambio negativo en y .

= Pendiente negativa correlación negativa

Un negativo pendiente demuestra una correlación negativa entre los siguientes:

las variables x e y

entrada y salida

variable independiente y la variable dependiente

causa y efecto

Correlación negativa se produce cuando las dos variables de un movimiento función en direcciones opuestas. A medida que el valor de x aumenta, el valor de y disminuye. Del mismo modo, como el valor de x disminuye, el valor de Y aumenta. Correlación negativa, entonces, indica una clara relación entre las variables, es decir, uno afecta al otro de una manera significativa.

En un experimento científico, una correlación negativa mostraría que un aumento en la variable independiente (el manipulado por el investigador) causaría una disminución en la variable dependiente (la medida por el investigador). Por ejemplo, un científico podría encontrar que a medida que los depredadores se introducen en un entorno, el número de presas se hace más pequeño. En otras palabras, existe una correlación negativa entre el número de depredadores y número de presas.

Ejemplos del mundo real

Un ejemplo sencillo de pendiente negativa en el mundo real está bajando una colina. Cuanto más lejos esté de viaje, cuanto más abajo se le cae. Esto puede ser representado como una función matemática, donde x es igual a la distancia recorrida y Y es igual a la elevación.

Otros ejemplos de pendiente negativa demuestran la relación entre dos variables:

Sr. Nguyen bebe café con cafeína dos horas antes de su hora de dormir. Los más tazas de café bebe (entrada), el menor número de horas que van a dormir (salida).

Aisha es la compra de un billete de avión. El menor número de días entre la fecha de compra y la fecha de salida (entrada), más el dinero Aisha tendrán que gastar en pasajes de avión (salida).

John está gastando una parte del dinero de su último cheque de pago en regalos para sus hijos. Cuanto más dinero gasta John (entrada), menos dinero John tendrá en su cuenta bancaria (de salida).

Mike tiene un examen al final de la semana. Desafortunadamente, él prefiere pasar su tiempo viendo deportes en la televisión que estudiar para el examen. Cuanto más tiempo pasa viendo la televisión Mike (entrada), la puntuación del Mike menor será en el examen (de salida). (En contraste, la relación entre el tiempo dedicado al estudio y la puntuación de examen estaría representada por una correlación positiva, ya que un aumento en el estudio conduciría a una mayor puntuación.)

water flows into a reservoir at a rate of 1500+7t^2 gallons/hour. Since there is a tiny hole in the reservoir, the water leaks out at a rate of 4t+t^2 gallons/hour. What is the net change in the amount of water in the reservoir over the time interval of [1,5]

Answers

9514 1404 393

Answer:

  6200 gallons

Step-by-step explanation:

The rate of change of volume is the difference between the inflow rate and the outflow rate.

  v'(t) = (1500 +7t^2) -(4t +t^2) = 6t^2 -4t +1500

The change in volume over the time interval of interest is the integral of this expression over that interval:

  [tex]\displaystyle\Delta V=\int_1^5{(6t^2-4t+1500)}\,dt=\left.(2t^3-2t^2+1500t)\right|^5_1\\\\=2(5^3-1^3)-2(5^2-1^2)+1500(5-1) = 2\cdot124-2\cdot24+1500\cdot4\\\\\boxed{\Delta V=6200\qquad\text{gallons}}[/tex]

The amount of water in the reservoir increases by 6200 gallons over the time interval.

What does > mean. Greater than or less than.

Answers

Answer:

less than

Step-by-step explanation:

The shoe store’s clerks are paid on commission. If the clerk receives a 12% commission on total purchase amounts before tax is applied, how much would the commission be for Isaac’s purchase with and without a coupon? (2 points)

plss show work I will mark brainliest

Answers

Answer:

a) 37 + 42 =79

=7/100 x 79

=553/100

=5.53

Isaac's total bill = 79 + 5.53 = $84.53

b) 25/100 x 79

= 19.75

= 79 - 19.75

= $59.25 (before tax)

7/100 x 59.25

= 414.75/100

= 4.15

= 59.25 + 4.15

= $63.4 (after adding tax)

First we have to take out the percentage of discount and minus it from the total cost . To find the discounted price with tax, we have to take out the percentage of the tax from the discounted amount and add it to the discounted amount to get the total cost.

A grocery store sells avocados for $1.25 each. The graph shows the cost for different numbers of avocados.

Drag each list, statement, or equation below to show whether it describes the independent quantity, the dependent quantity, or neither.

Answers

Answer:

A grocery store sells avocados for $1.25 each. The graph shows the cost for different numbers of avocados.

Drag each list, statement, or equation below to show whether it describes the independent quantity, the dependent quantity, or neither.

Step-by-step explanation:

6,726 ÷ 85
with the remainder

Answers

Answer:

79.13

Step-by-step explanation:

i need help for this question

Answers

Answer:

4, 4, and 8

Step-by-step explanation:

2 cups * 2 marshmallows per cup = 4 marshmallows

8 marshmallows / 2 marshmallows per cup = 4 cups of hot cocoa

16 marshmallows / 2 marshmallows per cup = 8 cups of hot cocoa

the rest of the space you need to fill in I think it’s 1,2 then 2,4 then 4,8 then 8,16 because your multiplying it by 2 each time. Hope this helps:)

Which ordered pair is a solution to the system of linear equations?


Can you please help me? I will mark biggest brain if correct. Thank you.​

Answers

B pretty simple need in depth let me know

Answer:

can u give me ur Intro..........

what is the percent of 2is 0.5​

Answers

Answer:

0.01

Step-by-step explanation:

Answer:

25

0.5 is what percent of 2 = 25.

Hope this helped! :)

May i have brainliest!

At a university, 60​% of the students who apply. Of the students the university​ accepts, 25% actually enroll If 2000 students​ apply, how many actually​ enroll?

Answers

Answer:

300 students are enrolled.

Step-by-step explanation:

As the university accepts 60% of the students who apply.

As 2000 students apply, it means that:

2000 × 60% ⇒ 2000 × 0.6 = 1200 students are accepted

Out of these 1200, 25% enrolled

1200 × 25% ⇒ 1200 × 0.25 = 300 students are enrolled

Therefore, 300 students are enrolled.

This equation has one solution. 3(x – 2) + 4x = 10(x + 1) What is the solution?
A.) -5
B.) -2
C.) -16/3
D.) -16/7

Answers

Answer:

C) -16/3

Step-by-step explanation:

3(x – 2) + 4x = 10(x + 1)

Multiply      3x-6+4x=10x+10

Combine like terms     7x-6=10x+10

Subtract 7x from both sides      -6=3x+10

Subtract 10 from both sides      -16=3x

Divide      -16/3=x

Answer:

Choice C -16/3

Step-by-step explanation:

3(x – 2) + 4x = 10(x + 1) <-- Distribute

3x - 6 + 4x = 10x + 10 <-- Combine all like terms

7x - 6 = 10x + 10 <-- Combine all like terms in one side

7x - 10x = 10 + 6 <-- Simplify

-3x = 16 <-- Isolate x by dividing

x = -16/3

I don't know what it means

Answers

Answer:   x + 1 = 15

Step-by-step explanation:

solve -

x= 15 - 1

x = 14

x is a variable so it's not fix value in math

PLEASE HELP ASAP. GIVE ANSWER AND BRIEF EXPLANATION.
The graph is attached
Determine whether the function shown in the graph is even or odd.

A. The function is even because it is symmetric with respect to the y-axis.
B. The function is odd because it is symmetric with respect to the y-axis.
C. The function is even because it is symmetric with respect to the origin.
D. The function is odd because it is symmetric with respect to the origin.

Answers

A. hope this helps):)

PLEASE HELP!!! In the diagram, line AB is a perpendicular bisector of segment CD. What is the length of CD?

Answers

Answer:

12

Step-by-step explanation:

AD is 6. a bisector splits a line in half. X would equal 6 meaning AD would equal 12.

Carlos can run 5 miles in 45 minutes, Kelly can run 10 miles in 80 minutes, and Mick can run 30 miles in 170 minutes

Answers

Answer:

60 min

Step-by-step explanation:

Answer:

what is the question please

I need help with this​

Answers

9514 1404 393

Answer:

  4

Step-by-step explanation:

Dilation centered at the origin multiplies each individual coordinate by the scale factor. Considering the x-coordinates of W and W', we have ...

  scale factor = Wx'/Wx = -12/-3 = 4

The dilation scale factor is 4.

A motorcycle bought for $10,000 depreciates continuously at 9% per annum. What is the value after seven years round the answer to the nearest dollar

Answers

Answer:

Book value= $62.83

Step-by-step explanation:

Giving the following information:

A motorcycle bought for $10,000 depreciates continuously at 9% per annum.

First, we need to calculate the depreciation of seven years:

FV= PV*{[1+(-i/100)]^n}

FV= 10,000*{[1+(-0.09/100)]^7}

FV= $9937.17

Book value= 10,000 - 9,937.17

Book value= $62.83

Please help brooo
Rose and Natalie are saving money for a trip. The table shows the amount of money Rose saves each month.
The graph shows Natalie's savings.

Please help



Which statement about rose and natiles is true

A the women save the same amount of money each month

B the initial value of natalies savings is greater than rose
C the rate of change ROC for roes saving is less than natiles

D after 5 months natalies has saved more money than rose

Answers

i believe it’s C because it looks like natalies roc is $60 while roses is only $50.

round 861 to the nearest ten. Enter your answer in the box below.​

Answers

860. Round down, since your ones place contains a 1.

please mark brainliest and have a great day

Answer:

860

Step-by-step explanation:

because it's rounding to the nearest ten and its only 1 you round it to 60

GIVING BRAINLIEST!
What kinds of observations can you make that might indicate a chemical change is taking place?

Answers

Answer:

1. Color Change.

2. Production of an odor.

3. Change of Temperature.

4. Evolution of a gas (formation of bubbles)

5. Precipitate (formation of a solid)

Step-by-step explanation:


4.1 Unit Rates
Find each unit rate. Round to the nearest hundredth, if nece
1. $140 for 18 ft?

Answers

Answer: 17.5

Step-by-step explanation:

what is the distance between the points (-6,7) and (-1,1)?

Answers

Answer:

8

Step-by-step explanation:

The user above is correct. The square root of 61 is equal to 7.810249676 which can be rounded up to 8.

Please Help Meee!!

11. A Fruit punch recipe contains 8 ounces of pineapple juice and makes enough punch for 20 servings

(a) If 150 servings need to be prepared for a party, how many ounces of pineapple juice are needed?

(b) How many servings will 20 ounces of pineapple juice produce? ​

Answers

A. There will be 60 ounces of pineapple juice needed. 150 servings divided by 20 servings is 7.5 servings. 7.5 servings times 8 ounces is 60 ounces.

B. You can make 50 servings of punch. 20 servings divided by 8 ounces is 2.5 ounces. 2.5 ounces times 20 ounces equals 50 servings.

Convert 45°C to Fahrenheit

Answers

It’s 113 Fahrenheit

Answer:

113

Step-by-step explanation:

it right trust

What is the slope of the line?

Answers

Answer:

24'

Step-by-step explanation:

the slop aims for the angle in which the 78 can go in: hope this helps!!

Ok so the slope of this line is approximately (2,1)

A child weighs 83 pounds. Given that 1 pound is equal to 16 ounces, how many ounces does the child weigh? A. 1,228 ounces B. 1,328 ounces 1,411 ounces D. 1,584 ounces C. A ir 100% of what numhor?​

Answers

a , sorry i just needed the point to ask questions

anyone wanna be friends boys or girls:)

Answers

Sure we can be friends

Answer:

sure follow my insta uknow.dan28

Step-by-step explanation:

Thien and her friends earned $80 washing cars. Thien received $30 from this amount.
What is Thien's share as a percentage of the total amount earned?

Answers

37.5%

You can just do 30/80

Mr. Rodriguez has owned his truck for 3 months. In that time, he has driven the truck a total of 45 miles.

How many miles has Mr. Rodriguez driven his truck in the 3 months?

Answers

Answer:

45 miles

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

45 divided by 3 is 15

sorry, i'm not all that good when it comes to explaining things. just kept it simple:)

If f(x) = x2 – 7x - 13 ; find the following.
find f(10)

Answers

F(x) = y
10= x2 - 7x -13
10= -5x -13
-10 -10
5x = -23


Answer is X = -23/5 or -4.6



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