Question

There are 12 candidates running for any of 6 distinct positions in a school's student council. In how many different ways could the 6 positions be filled?

Answer 1

Answer:

$Ways = 665280\ ways$

Step-by-step explanation:

Given

$Candidates = 12$

$Positions = 6$

Required

Determine the number of ways to fill the vacant position

The first position can be any of the 12 candidates;

The next candidate can be any of the remaining 11

The next candidate can be any of the remaining 10

The next candidate can be any of the remaining 9

The next candidate can be any of the remaining 8

The next candidate can be any of the remaining 7

So: we have;

$Ways= 12 * 11 * 10 * 9 * 8 * 7$

$Ways = 665280\ ways$

Answer 2

Answer:

3991680

Step-by-step explanation:

The questions asks for the number of ways to select and arrange 7 objects from a group of 12 objects. Substitute n=12 and r=7 into the permutation formula P(n,r)=n!(n−r)! to find that P(12,7)=12!(12−7)!=12!5!=3,991,680. There are 3,991,680 possible ways in which candidates could be chosen to fill the positions.