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Help!! Permutations and Combinations

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Junior | Next Rank: 30 Posts
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by cfarrera » Thu May 14, 2009 7:08 pm
I got these problems from a friend's GMAT notes, but I had a problem aproaching them mostly because a fiend permutations and combinations a bit confusing:

1. How many ways can a 3 person committe be formed from 4 couples if both members of a couple can't be on the committe?

2. In how many ways can you arrange 6 persons (3 women and 3 men) who are sitted in a circle if Laura has to be sitted either beside the T.V. or beside the door, which are opposite to each other, and two men cannot sit next to each other?

Thanks for your feedback
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Junior | Next Rank: 30 Posts
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by zeal_huyi » Fri May 15, 2009 5:27 am
1. Pick the committee one by one. The first committee will have 8 choices since you will be picking from 8 people. After you picked the first committee, you can't pick his/her spouse. Then you will only have 6 choices left for the second member. Apply the same logic for the third member. You multiply the number of choice together. You get 8 * 6 * 4 = 48 * 4 = 192.

2. Not clear of what you mean by Laura has to be seated either beside the TV or door. I assume those 2 objects would be fixed. Depending on what you mean by arranging in a circle. I would assume that as long as their relative position doesn't change then it is still consider to be the same arrangement. But what is tricky here is Laura has to sit next to TV or door which are fix objects. Can you double check the question again?
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