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In how many ways can a commitee of 4 women and 5 men

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In how many ways can a commitee of 4 women and 5 men [#permalink] New post 24 Aug 2012, 08:02
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

57% (03:22) correct 43% (03:38) wrong based on 34 sessions
In how many ways can a committee of 4 women and 5 men be chosen from 9 women and 7 men, if Mr.A refuses to serve on the committee if Ms.B is a member??

A. 1608
B. 1860
C. 1680
D. 1806
E. 1660
[Reveal] Spoiler: OA

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Re: In how many ways can a commitee of 4 women and 5 men [#permalink] New post 24 Aug 2012, 09:16
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rajathpanta wrote:
In how many ways can a committee of 4 women and 5 men be chosen from 9 women and 7 men, if Mr.A refuses to serve on the committee if Ms.B is a member??

A. 1608
B. 1860
C. 1680
D. 1806
E. 1660


Total number of ways a committee of 4 women and 5 men can be chosen from 9 women and 7 men is C^4_9*C^5_7=2,626.

The number of committees with Mr.A and Mr.B is C^1_1*C^1_1*C^3_8*C^4_6=840.

The number of committees which do not have Mr.A and Mr.B (together) is 2,646-840=1,806.

Answer: D.
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Re: In how many ways can a commitee of 4 women and 5 men [#permalink] New post 28 Aug 2012, 00:43
Bunuel wrote:
rajathpanta wrote:
In how many ways can a committee of 4 women and 5 men be chosen from 9 women and 7 men, if Mr.A refuses to serve on the committee if Ms.B is a member??

A. 1608
B. 1860
C. 1680
D. 1806
E. 1660


Total number of ways a committee of 4 women and 5 men can be chosen from 9 women and 7 men is C^4_9*C^5_7=2,626.

The number of committees with Mr.A and Mr.B is C^1_1*C^1_1*C^3_8*C^4_6=840.

The number of committees which do not have Mr.A and Mr.B (together) is 2,646-840=1,806.

Answer: D.


Thanks Bunuel for explanation, it is faster and clearer way (BTW i think there is typo its not 2,626). I have tried to think from different way, let say number of ways whithout Ms.B 9C5-8C3=70 is multiplied to number of commities with men which is 21 so overall 1470. Could you please clarify where i got wrong?
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Re: In how many ways can a commitee of 4 women and 5 men [#permalink] New post 28 Aug 2012, 10:22
bunuel.. question is saying if A will be the member then B will not.. but wat u did is that both will not be the member..

if we do ...8c3 *7c5 =?? in that b will not join but A will join..

if we do.. 9c4*6c4?? ..in this we l not have a will join??

wat actually m i asking cant we do with this way??
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Re: In how many ways can a commitee of 4 women and 5 men [#permalink] New post 29 Aug 2012, 00:46
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sanjoo wrote:
bunuel.. question is saying if A will be the member then B will not.. but wat u did is that both will not be the member..

if we do ...8c3 *7c5 =?? in that b will not join but A will join..

if we do.. 9c4*6c4?? ..in this we l not have a will join??

wat actually m i asking cant we do with this way??


All committees are good but the committees which have Mr.A and Ms.B together. So, we found the number of all committees possible and subtracted the number of committees with Mr.A and Ms.B in them.

We could solve the question with direct approach as well, though it would be lengthier:

The number of committees with Ms.B but without Mr.A is C^3_8*C^5_6;

The number of committees without Ms.B but with Mr.A is C^4_8*C^4_6;

The number of committees without Ms.B and without Mr.A is C^4_8*C^5_6;

Total: C^3_8*C^5_6+C^4_8*C^4_6+C^4_8*C^5_6=1,806.

Hope it's clear.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In how many ways can a commitee of 4 women and 5 men [#permalink] New post 26 Aug 2014, 03:44
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Re: In how many ways can a commitee of 4 women and 5 men   [#permalink] 26 Aug 2014, 03:44
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