Question

There are 15 candidates for 4 job positions.

What is the total number of outcomes possible?
N

Answer 1

32760 ways

Explanation:

Given

Number of Candidates = 15

Job Positions = 4

Required:

Number of outcomes

This question represent selection; i.e. selecting candidates for job positions;

This question can be solved in any of the following two ways

Method 1.

The first candidate can be chosen from any of the 15 candidates

The second candidate can be chosen from any of the remaining 14 candidates

The third candidate can be chosen from any of the remaining 13 candidates

The fourth candidate can be chosen from any of the remaining 12 candidates

Total Possible Selection = 15 * 14 * 13 * 12

Total Possible Selection = 32760 ways

Method 2:

This can be solved using permutation method which goes thus;

`nPr = (n!)/((n-r)!)`

Where n = 15 and r = 4

So;

`nPr = (n!)/((n-r)!)` becomes

`15P4 = (15!)/((15-4)!)`

`15P4 = (15!)/(11!)`

`15P4 = (15*14*13*12*11!)/(11!)`

`15P4 = 15*14*13*12`

`15C4 = 32760`

Hence, there are 32760 ways