Question

g a club of 12 people would like to choose a person for each office of president, a vice president, and a secretary. How many different ways are there to select the officers so that only one person holds each office

Answer 1

220 possible ways

Explanation:

Given

`n = 12` --- people

`r = 3` -- posts
`(President, Vice\ President\ and\ Secretary)`

Required

Determine the number of selection

Since there is no condition attached, the number of selection is:

`Selection = ^nC_r`

Substitute values for n and r

`Selection = ^(12)C_3`

Apply combination formula

`Selection = (12!)/((12-3)!3!)`

`Selection = (12!)/(9!3!)`

`Selection = (12*11*10*9!)/(9!*3*2*1)`

`Selection = (12*11*10)/(6)`

`Selection = (1320)/(6)`

`Selection = 220`

Hence, there are 220 possible ways