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

Answer:

220 possible ways

Step-by-step 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

$Selection = \frac{12!}{(12-3)!3!}$

$Selection = \frac{12!}{9!3!}$

$Selection = \frac{12*11*10*9!}{9!*3*2*1}$

$Selection = \frac{12*11*10}{6}$

$Selection = \frac{1320}{6}$

$Selection = 220$

Hence, there are 220 possible ways