Combinatorics

[szDave]

Hello,

A certain company employs 6 senior officers and 4 junior officers. If a committee is to be created that is made up of 3 senior and 1 junior officer, how many different committees are possible?

a) 8
b) 24
c) 58
d) 80
e) 210

[Brent@GMATPrepNow]

Hello,

A certain company employs 6 senior officers and 4 junior officers. If a committee is to be created that is made up of 3 senior and 1 junior officer, how many different committees are possible?

a) 8
b) 24
c) 58
d) 80
e) 210

Take the task of creating the 4-person committee and break it into stages.

Stage 1: Select 3 senior officers
Since the order of the selected officers does not matter, we can use combinations.
We can select 3 officers from 6 senior officers 6C3 ways (= 20 ways)

Stage 2: Select 1 junior officer
There are 4 junior officers, so we can select 1 officer in 4 ways

By the Fundamental Counting Principle (FCP) we can complete the two stages (and thus select members for the committee) in (20)(4) ways ([spoiler]= 80 ways[/spoiler])

Answer = D

Cheers,
Brent

Aside: For more information about the FCP, we have a free video on the subject: https://www.gmatprepnow.com/module/gmat-counting?id=775

If anyone is interested, we have a free video on calculating combinations (like 6C3) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789