Asked by jiya
How to show that 2nCn <= 2^2n?
Answers
Answered by
Steve
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}.
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}.
Answered by
jiya
Thank you, but can u tell me how to prove it by induction?
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