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If C (N, 12) = C (N, 8), Then C (22, N) is Equal to (A) 231 (B) 210 (C) 252 (D) 303 - Mathematics

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MCQ

If C (n, 12) = C (n, 8), then C (22, n) is equal to

Options

  • 231

  • 210

  •  252

  • 303

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Solution

231

\[{}^n C_{12} =^n C_8\]
\[\Rightarrow n = 12 + 8 = 20\] [∵ \[{}^n C_x =^n C_y \Rightarrow n = x + y\ \text{or} x = y\]
Now,
\[{}^{22} C_n =^{22} C_{20}\]
\[= \frac{22}{2} \times \frac{21}{1}\]
\[= 231\]
Concept: Combination
  Is there an error in this question or solution?

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Q 5 | Page 25

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