Question

Nine comedy acts will perform over two evenings. Five of the acts will perform on the first evening wants can the schedule for the first evening be made?

Answer 1

Complete Question Statement:

Nine comedy acts will perform over two evenings. Five of the acts will perform on the first evening and the order in which the acts perform is important. How many ways can the schedule for the first evening be made?

Answer:

The schedule for the first evening can be made in $15120$ ways.

Step-by-step explanation:

To determine:

How many ways can the schedule for the first evening be made?

Fetching Information and Solution Steps:

As

• The number of comedy acts that will perform over two evenings = 9
• The number acts that will perform on the first evening = 5

As the order in which the acts perform is important, meaning order matters.

So, we will be using permutations to determine the number of ways the schedule for the first week be made.

So,

Using $n$ for the total number and $r$ for the number of spots, we can apply the formula as:

$P(n, r) = {\frac {n!}{(n-r)!}}$

$P(n, r) = {\frac {9!}{(9-5)!}}$

$P(n, r) = {\frac {9!}{4!}}$

$P(n, r) = \frac{9!}{4!}=9\cdot \:8\cdot \:7\cdot \:6\cdot \:5$

$P(n, r)=9\cdot \:8\cdot \:7\cdot \:6\cdot \:5$

$P(n, r)=15120$

Therefore, the schedule for the first evening can be made in $15120$ ways.

Keywords: permutations, combinations

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