Total number of arrangements = 5! = 120
Now the following is the scenario in which 2 Men are together,
MM---
-MM--
--MM-
---MM
Hence picking 2M from 2M = 2C2 = 1 way and arranging will be 2 ways. So for Men it would be 2 ways totally.
Selecting 3 women would be 3C3 = 1. The 3W can be arranged in 3! ways like MMW1W2W3 or MMW2W1W3 etc totally it will 6 ways similarly for all the 4 cases it would be 6*4 = 24 ways
Total arrangement where 2M are together = 24 * 2 = 48 ways.
Required arrangement = 120 - 48 = 72 ways.
Not sure if this is correct..
-Deepak
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Permutation & combination
Source: Beat The GMAT — Problem Solving |
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sureshbala
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Forget about the chairs.
All we need is to arrange 2 boys and 3 girls in a row such that boys are not together.
First we can arrange girls in 3! =6 ways
_ G2 _ G1 _ G3 _
Now the 2 boys can be seated in any of the 4 places available in 4P2 = 12 ways
Hence total number of ways = 6 x 12 = 72 ways
All we need is to arrange 2 boys and 3 girls in a row such that boys are not together.
First we can arrange girls in 3! =6 ways
_ G2 _ G1 _ G3 _
Now the 2 boys can be seated in any of the 4 places available in 4P2 = 12 ways
Hence total number of ways = 6 x 12 = 72 ways
