# UGC-NET | UGC NET CS 2016 July – III | Question 31

The number of different binary trees with 6 nodes is ______.**(A)** 6**(B)** 42**(C)** 132**(D)** 256**Answer:** **(C)****Explanation:** The number of different binary trees with 6 nodes is fact(2n) / fact(n+1) * fac(n) where n is no nodes:

If n= 6, then fact(2 * n) / fact(n+1) * fac(n) = fact(2 * 6) / fact(6 + 1) * fact(6) = fact(12) / fact(7) * fact(6) = 12 * 11 * 10 * 9 * 8 * fact(7) / fact(7) * fact(6) = 12 * 11 * 10 * 9 * 8 / 6 * 5 * 4 * 3 * 2 = 6 * 11 * 2 = 132.

So, option (C) is correct.

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