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In how many ways can 5 men and their 5 women be arranged on a bench such that (a) each...
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High School Teacher
First in case (a) you should look at each pair as one block since they must sit next to each other. You can arrange 5 pairs in 5!=120 ways. Then you can arrange man and woman in 2 ways (mw or wm) for each of 5 pairs.
Your result is `5! cdot 2^5=3840`
In case (b) you have 8 people and 1 pair which you can arrange in 9! ways and you can arrange man and woman in the pair in 2 ways (mw or wm).
Your result is `9! cdot 2=725760`
Posted by tiburtius on October 28, 2012 at 6:32 PM (Answer #1)
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