## A play needs three protagonists (a man, a woman, and a girl), two antagonists (a man and a woman), and two supporting roles (a man and a boy).

A play needs three protagonists (a man, a woman, and a girl), two antagonists (a man and a woman), and two supporting roles (a man and a boy).

Six men, six women, three boys, and four girls attended the auditions. The number of ways the roles can be cast is:

woman can be protagonists or antagonists

six women are there

2 women can be selected in ⁶C₂ = 15 ways and can be assigned role in 2! = 2 ways

Hence total ways role to woman can be assigned = 15 x 2 = 30

Man can be protagonists , antagonists , supporting role

six men are there

3 men can be selected in ⁶C₃ =20 ways and can be assigned role in 3! = 6 ways

Hence total ways role to woman can be assigned =20 x 6 = 120

Girl can be protagonists

There are 4 girls

Hence 4 ways

Boy can be supporting roles

There are 3 boys

Hence 3 ways

Total Ways = 30 x 120 x 4 x 3

= 43,200

The number of ways the roles can be cast is: 43200

## Here is a pyramid with a base that is a pentagon with all sides the same length.

Here is a pyramid with a base that is a pentagon with all sides the same length. Describe the cross section that will result if the pyramid is sliced

a. horizontally (parallel to the base)

b. vertically through the top vertex (perpendicular to the base)

## What is the quotient of (xº + 8) = (x + 2)? O x2 + 2x + 4 x² – 2x +

What is the quotient of (xº + 8) = (x + 2)?

O x2 + 2x + 4
x² – 2x + 4
o x² + 4
O x² – 4

## Determine the value(s) for which the rational expression −3z+66z2+14z−80 is undefined

Determine the value(s) for which the rational expression −3z+66z2+14z−80 is undefined

## For lines a, c, and d, line c is parallel to line d and m∠1 = 55°. : For the

For lines a, c, and d, line c is parallel to line d and m∠1 = 55°.

: For the given diagram, use the measure of ∠1 to find the measure of the remaining seven angles.
: In two or more complete sentences, explain the relationship between angle pairs a)∠1 and ∠7 and b)∠1 and ∠2. in your explanation, include how you calculated each of the angle measures in the special angle pairs.

## A person runs 1 4/5 miles in 1/5 of an hour determine how many miles they are running per hour

A person runs 1 4/5 miles in 1/5 of an hour determine how many miles they are running per hour

## Dostaniecie 5 gwiazdek i serce a może nawet naj jak odpowiecie na następujące pytanie: wypisz pięć kolejnych różnic od 0 wielokrotności

Dostaniecie 5 gwiazdek i serce a może nawet naj jak odpowiecie na następujące pytanie: wypisz pięć kolejnych różnic od 0

wielokrotności liczby 45:
wielokrotności liczby 18:
jaka jest najmniejsza wspólna wielokrotność liczb 45 i 18?

## 5 pounds of apples cost \$8.20. How much is it for 1 pound . free if you also my riidle

5 pounds of apples cost \$8.20. How much is it for 1 pound .

free if you also answer my riidle what goes and comes out it happends at dusk what is it A. sex B, poop C. nothing D. this is a stupid riddle

## After reading a book about ancient Egypt, Cassie decided to build a model of a pyramid out of cardboard. How much

After reading a book about ancient Egypt, Cassie decided to build a model of a pyramid out of cardboard.

How much cardboard does Cassie need to make the model, including the bottom?

## A triangle has side lengths of (6p-7) centimeters,(7p-2) centimeters and (6q-9) centimeters. Which expression represents the perimeter, in centimeters, of

A triangle has side lengths of (6p-7) centimeters,(7p-2) centimeters and (6q-9) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?