Question
Download Solution PDFIf nC9 = nC8 find nC17?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
nC9 = nC8
Formula Used:
nCr = \(\frac{n!}{r!(n - r)!}\)
Calculation:
We have,
nC9 = nC8
⇒ \(\frac{n!}{9!(n - 9)!} = \frac{n!}{8!(n - 8)!}\)
⇒ \(\frac{n!(n - 8)!}{n!(n - 9)!} = \frac{9!}{8!}\)
⇒ \(\frac{(n - 8)!}{(n - 9)!} = \frac{9!}{8!}\)
⇒ \(\frac{(n - 8)(n - 9)!}{(n - 9)!} = \frac{9 \times 8!}{8!}\)
⇒ n - 8 = 9
⇒ n = 17
Now we have to find nC17
Putting n = 17
⇒ 17C17
⇒ \(\frac{17!}{17!(17 - 17)!}\)
⇒ \(\frac{17!}{17! \times 0!}\)
⇒ \(\frac{17!}{17! \times 1}\)
⇒ 1
∴ The value of nC17 is 1
Last updated on May 26, 2025
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