A certain company employs 6 senior officers and 4 junior of

Question

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 officers and 1 junior officer, how many different committee are possible?

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

A. 8
B. 24
C. 58
D. 80
E. 210

Bunuel · Accepted Answer

C^3_6*C^1_4=80 : C^3_6 - # of ways to choose 3 different senior officers out of 6 and C^1_4 - # of ways to choose 1 junior officer out of 4. We multiply these two because if one event can occur in m ways and a second can occur independently of the first in n ways, then the two events can occur in mn ways (this is called Principle of Multiplication). Answer: D. For theory on combinatorics check: math-combinatorics-87345.html Hope it helps.

ScottTargetTestPrep · Answer

We need to determine how many different committees are possible with 3 senior officers and 1 junior officer from 6 senior officers and 4 junior officers. Let’s first determine the number of ways to select 3 senior officers.
 
number of ways to select 3 senior officers from 6 of them = 6C3 = (6 x 5 x 4)/3! = 20 ways
 
Next we can determine the number of ways to select 1 junior officer.
 
number of ways to select 1 junior officer from 4 of them = 4C1 = 4 ways
 
Thus the number of ways to select 3 senior officers and 1 junior officer is 20 x 4 = 80 ways.
 
Answer: D

gettinit · Answer

6!/3!(6-3)! = 20

4!/1!(4-1)!=4

so number of different committees equals 20*4=80

shashankism · Answer

Basically in this question we need to select 3 senior officer from the 6 senior officers available and 1 junior officer from 4 junior officers available.

This can be done in 6C3 * 4C1 ways 
=  * 
= 20*4 
= 80

Answer D

pushkarajnjadhav · Answer

There are 6 senior officers and 4 junior officers.
The committee contains 3 senior officers and 1 junior officer.

3 senior officers can be selected from 6 officers in 6C3 ways = (6 x 5 x 4)/3! = 20 ways
1 junior officers can be selected from 4 officers in 4c1 ways= 4 ways

Therefore total number of ways to select 3 senior and 1 junior officer are 20*4 =80 ways.
Hence Answer is D.

Kudos if it helps.

BrentGMATPrepNow · Answer

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 (= 80 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.

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CAMANISHPARMAR · Answer

The order is not important hence this is a combinations questions.

The number ways in which a committee can be made with 3 senior officers and 1 junior officer in each committee is in 6C3 * 4C1 = 80 ways.

Option D is the correct answer

Archit3110 · Answer

combination
6c3*4c1 = 20*4 ; 80
IMO D

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A certain company employs 6 senior officers and 4 junior of

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