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Question

Mathematics Question on permutations and combinations

If  nC12\, {{^n C}_{12}} = nC8\, {{^n C}_8} then nn is equal to

A

26

B

12

C

6

D

20

Answer

20

Explanation

Solution

We know that.
If nCx=nCy{ }^{n} C_{x}={ }^{n} C_{y}, then
(i) x=yx=y
(ii) x+y=nx + y = n
∴nC12=nC8\therefore { }^{n} C_{12}={ }^{n} C_{8}
⇒n=12+8=20\Rightarrow n=12+8=20