SOLUTION: How do I solve for n? C(n, 5) = C(n, 7)

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Question 573959: How do I solve for n? C(n, 5) = C(n, 7)
Found 2 solutions by solver91311, richard1234:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


If you consider all of the possibilities for various combinations of things taken at a time and listed them in desceding order of , you would get a list that looks like:



















(Since , these two list items must be equidistant from the middle item in the list.)


















But since the s must all be integers, there can only be one item in the list between 7 and 5, namely



hence



So




John

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Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Use the identity that C(n, k) = C(n, n-k). Here, we can let k = 5, n - k = 7. From here we get n - 5 = 7, n = 12.