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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