+275 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.
+289 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.
