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Sunday, 7 August 2011
Math GRE - #6
When 20 children in a classroom line up for lunch, Pat insists on being somewhere ahead of Lynn. If Pat's demand is to be satisfied, in how many ways can the children line up?
Solution :
To order the children without considering Pat's demand, the answer would be 20!. In half of these permutations, Pat is ahead of Lynn. In the other half, Pat is behind Lynn. Therefore, the answer is \frac{20!}{2}.
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