Our club has 10 members, and wishes to pick a president, secretary, treasurer, morale officer, and dog catcher. In how many ways can we choose the officers, if individual members can only hold at most one office?

Guest Jan 8, 2021

#1**+1 **

10 ways to pick pres

9 ways to pick secretary

8 ways to pick treasurer

7 ways to pick morale officer

6 ways to pick dog catcher

30240 ways

:D

AvenJohn Jan 8, 2021

#2**0 **

I think you must of meant "..no person can hold 'more than' 1 office..."

This is the case of the number of "different" ways to select 4 items out of 10.

where the order matters (who holds the president office matters) and no repetition is allowed. This is a permutation problem

--

so there are 10 choices for president

then after that there are 9 choices for VP

then afte P and VP there are 8 choices for Treasurer

and finally after P, VP and T, there are 7 choices left for Secretary.

So the number of ways to fill those offices with 10 candidates is

\(\frac{10!}{(10-4)!}\)

10*9*8*7*6

30240

hihihi Jan 8, 2021