If nC9 = nC8 find nC17?

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AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 2)
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  1. 17
  2. 9
  3. 2
  4. 1

Answer (Detailed Solution Below)

Option 4 : 1
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Detailed Solution

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Given:

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

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