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How many ways are there for 3 males and 3 females to sit

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How many ways are there for 3 males and 3 females to sit [#permalink] New post 18 Dec 2010, 04:18
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69% (01:53) correct 31% (01:00) wrong based on 64 sessions
How many ways are there for 3 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?

A. 6
B. 12
C. 72
D. 100
E. 720
[Reveal] Spoiler: OA
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Re: Circular table [#permalink] New post 18 Dec 2010, 05:22
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Expert's post
zisis wrote:
How many ways are there for 3 males and 3 females to sit if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?

6
12
72
100
720


I guess they sit around the table as you mention it in the title of the topic.

So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 3 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 3! different ways, so total 2*3!=12.

Answer B.
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Re: Circular table [#permalink] New post 20 Sep 2013, 00:34
Bunuel wrote:
zisis wrote:
How many ways are there for 3 males and 3 females to sit if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?

6
12
72
100
720


I guess they sit around the table as you mention it in the title of the topic.

So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 3 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 3! different ways, so total 2*3!=12.

Answer B.


Lets first sit the 3 man, 2! ways.

Now since one position is fixed for women, there are 2 women left and they have 2! ways

2! X 2! = 4 answer is diff this way.

or shall we give possibility of 3 ways for women to be fixed with back facing so 3! ways, Lets discuss the doubt.

If u like my way of discussion plz give Kudos.
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Re: Circular table [#permalink] New post 20 Sep 2013, 00:43
Expert's post
honchos wrote:
Bunuel wrote:
zisis wrote:
How many ways are there for 3 males and 3 females to sit if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?

6
12
72
100
720


I guess they sit around the table as you mention it in the title of the topic.

So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 3 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 3! different ways, so total 2*3!=12.

Answer B.


Lets first sit the 3 man, 2! ways.

Now since one position is fixed for women, there are 2 women left and they have 2! ways

2! X 2! = 4 answer is diff this way.

or shall we give possibility of 3 ways for women to be fixed with back facing so 3! ways, Lets discuss the doubt.

If u like my way of discussion plz give Kudos.


Since Mary's position is fixed men can be seated in 3! ways not in 2! ways. Would be easier to draw a circle and count the possible arrangements.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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.


What are GMAT Club Tests?
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Re: Circular table   [#permalink] 20 Sep 2013, 00:43
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