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A committee of three biology professors, two physics professors, and f
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22 Nov 2021, 08:35
22 Nov 2021, 08:35
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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
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Re: A committee of three biology professors, two physics professors, and f
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22 Nov 2021, 09:35
22 Nov 2021, 09:35
1
Carcass wrote:
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
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
General Discussion
Re: A committee of three biology professors, two physics professors, and f
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22 Nov 2021, 08:44
22 Nov 2021, 08:44
No of different committees = \(^4C_3* ^5C_2* ^6C_4 = ^4C_{4-3}* ^5C_2* ^6C_{6-4} = ^4C_1* ^5C_2* ^6C_2 = 4*(\frac{5*4}{2*1})*(\frac{6*5}{2*1}) = 4*10*15 = \textbf{600}\)
Hence, Answer is D
Hence, Answer is D
