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Write the following expression as a single combination n choose k so that k is not equal to 1 and n-k is not equal to 1.

1/5 * 50 choose 10 = ? choose ?

You cannot just multiply the 2 numbers. I think pascal's identity could be used here.

 Sep 5, 2022
 #1
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There is definitely no relation to pascal's identity  in this problem. That identity would be used, when there is a sum rather than a product.

 

50 C 10 = (50 * 49 * 48 * 47 * 46 * 45 * 44 * 43 * 42 * 41)/(10!).

Multiplying 1/5 to 50 gives us:

 

(10 * 49 * 48 * 47 * 46 * 45 * 44 * 43 * 42 * 41)/(10 * 9 .... * 1). The 10 terms cancel out. 

 

(49 * 48 * 47 .... * 41)(9 * 8 *... * 1)  = 49 C 9.

 Sep 5, 2022

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