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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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