If n^C12 = n^C6, then the value of in is?
- 12
- 14
- 16
- 18
Explanation
The combination formula is:
nCr = n! / (r!(n-r)!)
Given that nC12 = nC6, we can equate the two expressions:
n! / (12!(n-12)!) = n! / (6!(n-6)!)
Simplifying the equation, we get:
12!(n-12)! = 6!(n-6)!
Since 12! = 12 × 11 × 10 × 9 × 8 × 7 × 6!, we can cancel out the 6! terms:
12 × 11 × 10 × 9 × 8 × 7 = (n-6)(n-7)(n-8)(n-9)(n-10)(n-11)
This equation is true when n = 18.
Therefore, the correct answer is 18.
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