# The drama club is holding auditions for 5 different parts in a one-act play. if 9 people audition, how

###### Question:

## Answers

The roles can be assigned in 15120 ways.

Step-by-step explanation:

The parts, which means that the order in which the people are selected is important. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this question:

5 people chosen from a set of 9. So

[tex]P_{(9,5)} = \frac{9!}{(9-5)!} = 15120[/tex]

The roles can be assigned in 15120 ways.

84 ways

Step-by-step explanation:

Given

Total individuals = 9

Available roles = 5

Required

Number of ways roles can be assigned.

First, it'll be assumed that no two individual shares a role and no single individual takes two roles.

Having said this, the number of ways the roles can be assigned can be calculated using the combination formula; as follows.

ⁿCr = C(n,r)

Where n represents the total individuals

n = 9

r represents the available roles

r = 5

So,

ⁿCr = C(n,r) =>

⁹C₆ = C(9,6)

⁹C₆= 9!/((9-6)!6!)

⁹C₆ = 9!/(3!6!)

⁹C₆ = (9 * 8 * 7 * 6!)/(6! * 3 * 2 * 1)

⁹C₆ = (9 * 8 * 7)/(3 * 2 * 1)

⁹C₆ = 504/6

⁹C₆ = 84

Hence, 9 roles can be assigned to 5 people in 84 ways

B

Step-by-step explanation:

I got it correct