Question

Permutations vs combinations(one step):

The bowling team at Lincoln High School must choose a president, vice
president, and secretary. If the team has 15 members, which expression could
be used to determine the number of ways the officers could be chosen?

Answer 1

the expression is:
`^(15)P_3=(15!)/((15-3)!)`

and 2730 different ways are possible.

Explanation:

In the given question we have to choose a president, vice

president, and secretary.

Permutations are used when order is important so, as in the given question order is required. We would use permutations

The formula used is:
`^nP_r=(n!)/((n-r)!)` where:

n=total number of objects

r=number of objects selected

In our case: n=15, r=3

Putting values and finding the answer:

`^nP_r\\^(15)P_3=(15!)/((15-3)!) =2730 \ ways`

So, the expression is:
`^(15)P_3=(15!)/((15-3)!)`

and 2730 different ways are possible.