What is the difference between the number of three-member committees

Question

What is the difference between the number of three-member committees that can be formed from a group of nine members and the total number of ways there are to arrange the members of such a committee?

A. 0
B. 84
C. 252
D. 420
E. 504

alldaytestprep · Answer

Number of ways to choose 3 from 9 = 9C3 = (9!)/(6! * 3!) --------> 84

Number of ways to arrange 3 people = 3 * 2 * 1 -----------------> 6 
----> Therefore each of our 84 3-person committees has 6 arrangments for 6 * 84 ----> 504 total arrangements

504 - 84 = 420

Answer: D

I still contend that "ways there are to arrange the members of such a committee" can be interpreted as how many ways can any given committee be arranged which would give an answer of 84 - 6 = 78.

Mirza13 · Answer

1st......9C3=84 2nd.....84×3!=504 therefore, difference is 504-84=420

EgmatQuantExpert · Answer

Solution

To find:  
 • The difference between the number of 3-members committee that can be formed from a group of 9 members and the total number of ways to arrange them

Approach and Working:   
 • Number of ways a committee of 3 members can be formed from a group of 9 members =  ^9C_3 
• Total number of ways to arrange the members =  ^9C_3 * 3! 
• Therefore, the difference =  ^9C_3 * 3! – ^9C_3 = ^9C_3 * 5 = 84 * 5 = 420

Hence, the correct answer is option D.

Answer: D

apurv09 · Answer

no of ways in which the community can be formed- 9C3= 9!/3!6!= 84
no pf ways in which it can be arranged =9P3= 9!/6!= 514

the difference= 420.
Answer D.

Please point out the flaws in my approach , if any.

ScottTargetTestPrep · Answer

The number of 3-member committees that can be formed from 9 people (i.e., order doesn’t matter) is 9C3 = 9!/(3! x 6!) = (9 x 8 x 7)/3! = (9 x 8 x 7)/(3 x 2) = 3 x 4 x 7 = 84.

The number of ways to form the committees and arrange the members (i.e., order matters) is 9P3 = 9 x 8 x 7 = 504.

Thus, the difference is 504 - 84 = 420.

Answer: D

EMPOWERgmatRichC · Answer

Hi All,

To start, the wording of this prompt is 'clunky' - and the GMAT writers word their questions in a far more rigorous and specific fashion than what we see here. That having been said, the basic concepts involved here are Combinations and Permutations.

We're asked for the difference between the number of three-member committees that can be formed from a group of nine members and the total number of ways there are to arrange the members of such a committee. The intent of this question is to ask for the difference in the number of possible 3-person groups and the number of ways to arrange 3 of the 9 people 'in a row.'

For the number of 3-person groups, we can use the Combination Formula: N!/K!(N-K)! = 9!/3!(9-3)! = (9)(8)(7)/(3)(2)(1) = 504/6 = 84

The number of ways to arrange 3 of the 9 people in a row = (9)(8)(7) = 504

The difference is 504 - 84 = 420

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

anirchat · Answer

The wording seems not GMAT standardized here. 
The total number of ways there are to arrange the members of such a committee -> Essentially means how many ways can we arrange the members of such a committee. (9P3 , Too difficult to digest)

What is the difference between the number of three-member committees

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What is the difference between the number of three-member committees

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