Question

A president, treasurer, and secretary, all di erent, are to be chosen from a club consisting of 12 people (whose names are I, J, K, L, M, N, O, P, Q, R, S, and T). How many di erent choices of ocers are possible if: (a) There are no restrictions

Answer 1

There are 220 choices

Explanation:

Given

`People = 12`

`Selection =3` (President, Treasurer and Secretary)

Required

Determine number of selection (if no restriction)

This is calculated using the following combination formula:

`^nC_r = (n!)/((n - r)!r!)`

Where

`n = 12`

`r= 3`

So, we have:

`^nC_r = (n!)/((n - r)!r!)`

`^(12)C_3 = (12!)/((12 - 3)!3!)`

`^(12)C_3 = (12!)/(9!3!)`

`^(12)C_3 = (12*11*10*9!)/(9!3!)`

`^(12)C_3 = (12*11*10)/(3!)`

`^(12)C_3 = (12*11*10)/(3*2*1)`

`^(12)C_3 = (12*11*10)/(6)`

`^(12)C_3 = 2*11*10`

`^(12)C_3 = 220\ ways`

There are 220 choices