Question

In how many ways can the first 4 guests arrive at a party if 15 guests have been invited.

Answer 1

the first 4 guests can arrive in 32,760 ways.

Explanation:

how many ways can the first 4 guests arrive at a party if 15 guests have been invited.

Permutations formula:

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

`P_((n,x)) = (n!)/((n-x)!)`

4 guests from a set of 15

P(15,4) = 15 * 14 * 13 * 12

= 32760

Therefore, the first 4 guests can arrive in 32,760 ways.

Answer 2

The first 4 guests can arrive in 32,760 ways.

Explanation:

The order in which the guests arrive is important. For example, A,B,C,D is a different outcome to B,A,C,D. 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:

`P_((n,x)) = (n!)/((n-x)!)`

In this question:

4 guests from a set of 15. So

`P_((15,4)) = (15!)/((15-4)!) = 32760`

The first 4 guests can arrive in 32,760 ways.