What is the number of different ways to choose a chairman, : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 17 Jan 2017, 12:32

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the number of different ways to choose a chairman,

Author Message
TAGS:

Hide Tags

Senior Manager
Joined: 24 Jul 2009
Posts: 297
Followers: 3

Kudos [?]: 130 [0], given: 0

What is the number of different ways to choose a chairman, [#permalink]

Show Tags

28 May 2010, 13:09
00:00

Difficulty:

25% (medium)

Question Stats:

100% (02:12) correct 0% (00:00) wrong based on 2 sessions

HideShow timer Statistics

What is the number of different ways to choose a chairman, two deputies, and two assistants for the class committee out of 7 students up for elections.

Which solution is correct ? And Why ?

A) $$7C1$$ * $$6C1$$ * $$5C1$$ * $$4C1$$* $$3C1$$
B) $$7C1$$ * $$6C2$$ * $$4C2$$
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36540
Followers: 7072

Kudos [?]: 93016 [0], given: 10541

Show Tags

28 May 2010, 14:09
nverma wrote:
What is the number of different ways to choose a chairman, two deputies, and two assistants for the class committee out of 7 students up for elections.

Which solution is correct ? And Why ?

A) $$7C1$$ * $$6C1$$ * $$5C1$$ * $$4C1$$* $$3C1$$
B) $$7C1$$ * $$6C2$$ * $$4C2$$

Correct answer is B: $$C^1_7*C^2_6*C^2_4=630$$.

$$C^1_7$$ - # of ways to choose 1 chairmen out of 7;
$$C^2_6$$ - # of ways to choose 2 deputies out of 6 members left;
$$C^2_4$$ - # of ways to choose 2 assistants out of 4 members left.

Answer A is not correct because it's counting # of different ways to choose 2 deputies out of 6 as $$C^1_6*C^1_5$$ (and next # of ways to choose 2 assistants out of 4 as $$C^1_4*C^1_3$$) which is not right. $$C^1_6*C^1_5$$ will have duplications in it and needs to be divided by 2! (# of peoples), which then gives the same answer as $$C^2_6$$.

Consider this: in how many different ways we can choose 2 different letters out of A, B, and C?

AB
AC
BC

Only 3, which can be obtained by $$C^2_3=3$$, another way would give incorrect answer - $$C^1_3*C^1_2=6$$.

The original question can be solved in another way:
Members: 1 - 2 - 3 - 4 - 5 - 6 - 7. Positions: C (chairmen), D (deputy), D (deputy), A (assistant), A (assistant), N (no position), N (no position): CDDAANN. # of ways to assign each letter (each position) to the members would be the # of permutations of 7 letters CDDAANN = $$\frac{7!}{2!2!2!}=630$$.

1-2-3-4-5-6-7
C-D-D-A-A-N-N
D-C-D-A-A-N-N
D-D-C-A-A-N-N
...
...

Hope it helps.
_________________
Re: Choose committee   [#permalink] 28 May 2010, 14:09
Similar topics Replies Last post
Similar
Topics:
8 There are different 10 circles. What is the number of the greatest pos 3 29 Apr 2016, 19:16
2 Mr. Jones is the Chairman of a committee. In how many ways can a commi 3 12 Sep 2015, 03:22
What is the maximum number of different pieces that 4 linear 1 04 Jul 2012, 11:55
1 How many different ways...? 6 25 Mar 2011, 14:12
14 The number of ways in which 8 different flowers can be 10 03 Dec 2007, 08:43
Display posts from previous: Sort by

What is the number of different ways to choose a chairman,

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.