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.


Quiz of this Question

My Personal Notes arrow_drop_up