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Given a sequence $ {a_1, a_2, ..., a_n} $ and a number k I have to find the number of subsequences with k elements, containing the element $ a_k $. I know that the total number of all subsequences is $ 2^n $, but it doesn't seem to be very helpful here.

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up vote 2 down vote accepted

If you are given that each sequence contains $a_k$ and you have $k$ elements total in the sequence, you only need $k-1$ other elements to fill up the rest of your sequence with, and you have $n-1$ other elements to choose from. It should be easier to count when you think about it like this.

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Is the answer just $ C^{k-1}_{n-1}?$ – Ormi Nov 24 '12 at 23:06
    
@UchihaMadara exactly! – Tom Oldfield Nov 25 '12 at 0:22

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