How to show that 2nCn <= 2^2n?

Answer 1

Suppose you have a set with 2n elements. How many subsets can we form? 2^{2n} = 4^n.

Now how many subsets, each containing exactly n elements, can we form? This number is {2n choose n}.

In the first statement above, we considered all subsets (not just those with n elements), and so 4^n is greater than or equal to {2n choose n}.

Answer 2

Thank you, but can u tell me how to prove it by induction?