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+16 votes

Match the pairs in the following questions by writing the corresponding letters only.

(A). The number distinct binary trees with $n$ nodes. (P). $\frac{n!}{2}$
(B). The number of binary strings of length of $2n$ with an equal number of $0’s$ and $1’s$. (Q). $ \binom{3n}{n}$
(C). The number of even permutation of $n$ objects. (R). $\binom{2n}{n}$
(D). The number of binary strings of length $6n$ which are palindromes with $2n$  $0’s$. (S). $\frac{1}{1+n}\binom{2n}{n}$
asked in Combinatory by Veteran (59.4k points)
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2 Answers

+20 votes
Best answer

(A) - S Catalyn no

(B) - R. Choosing n locations out of 2n to place 0. Remaining automatically become 1.

(C) -P An even permutation is a permutation obtainable from an even number of two-element swaps, For a set of n elements and n>2, there are n!/2 even permutations. Ref ->

(D) -> Q 

Length = 6n, as it is palindrome, we need to only consider half part.

Total Length to consider 3n (Remaining 3n will be revese of this 3n)

now Choosing n 0's out of 3n. So Q is correct for D.

answered by Boss (42.4k points)
selected by
+1 vote

A - S
B - R
C - P
D - Q
answered by Boss (34.2k points)

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