A committee of three biology professors, two physics professors, and

Question

A committee of three biology professors, two physics professors, and four chemistry professors is to be made in a college. If the college has four, five, and six professors of biology, physics, and chemistry respectively, how many different committees are possible?

A. 120
B. 240
C. 300
D. 600
E. 720

A. 120
B. 240
C. 300
D. 600
E. 720

BrentGMATPrepNow · Accepted Answer

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

Stage 1 : Select 3 biology professors to be on the committee 
There are 4 biology professors to choose from. 
Since the order in which we select the biology professors does not matter, we can use combinations. 
We can select 3 biology professors from 4 biology professors in 4C3 ways (4 ways)
So, we can complete stage 1 in  4  ways

Aside: The video below shows how to quickly calculate combinations (like 4C3) in your head.

Stage 2 : Select 2 physics professors to be on the committee 
There are 5 physics professors to choose from. 
Since the order in which we select the physics professors does not matter, we can use combinations. 
We can select 2 physics professors from 5 physics professors in 5C2 ways (10 ways)
So, we can complete stage 2 in  10  ways 
 
 Stage 3 : Select 4 chemistry professors to be on the committee 
There are 6 chemistry professors to choose from. 
Since the order in which we select the chemistry professors does not matter, we can use combinations. 
We can select 4 chemistry professors from 6 chemistry professors in 6C4 ways (15 ways)
So, we can complete stage 3 in  15  ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create the committee) in  (4)(10)(15)  ways (= 600 ways)

Answer: D

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

RELATED VIDEOS
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saransh2797 · Answer

Hi Bunuel, In this question, when we use counting method, we are dividing to account for the repititions. However, it was not explicitly mentioned that All Biology professors are similar. This is some confusion with many PnC questions because sometimes it is assumed that the objects are different and sometimes it is assumed that objects are same, please help

Bunuel · Answer

People are distinct! How can they not be? Having Biology Professor A in the committee is different from having Biology Professor B. This is a fairly straightforward question.

We have:
• Biology = 4 professors
• Physics = 5 professors
• Chemistry = 6 professors

We need:
• 3 from Biology
• 2 from Physics
• 4 from Chemistry

So, the total number of different committees is 4C3 * 5C2 * 6C4 = 4 * 10 * 15 = 600. Here, for example, 4C3 gives the number of groups of 3 different professors chosen from 4.

A committee of three biology professors, two physics professors, and

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A committee of three biology professors, two physics professors, and

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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