Bunuel wrote:
A company consists of 5 senior and 3 junior staff officers. If a committee is created with 3 senior and 1 junior staff officers, in how many ways can the committee be formed?
(A) 12
(B) 30
(C) 45
(D) 80
(E) 200
Kudos for a correct solution.
Take the task of creating the committee and break it into
stages.
Stage 1: Select 3 senior officers for the committee
Since the order in which we select the senior officers does not matter, we can use combinations.
We can select 3 senior officers from 5 senior officers in 5C3 ways (10 ways)
So, we can complete stage 1 in
10 ways
If anyone is interested, we have a free video on calculating combinations (like 5C3) in your head: [url]
http://www.gmatprepnow.com/module/gmat- ... /video/789Stage 2: Select 1 junior officer for the committee
There are 3 junior officers to choose from, so we can complete this stage in
3 ways.
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a 4-person committee) in
(10)(3) ways (= 30 ways)
Answer: B
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video:
http://www.gmatprepnow.com/module/gmat-counting/video/775
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