Question

Asked Sep 8, 2019

Show that

n n

( ) = ( ).

k n - k

Give an interpretation involving subsets.

Step 1

To interpret (hence prove) the given equality of the two binomial coefficients, using set theory

Step 2

First let us look at an example; the same proof will apply to the general case. In the example, n is 5 and k is 2, n-k is 3. The left hand side is the number of subsets of 2 elements from a set of 5 elements. Every time w...

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