COMEDK · Maths · 4. Permutation Combination
\(\text { Find }{ }^n C_{21} \text {, if }{ }^n C_{10}={ }^n C_{12}\)
- A 21
- B 2
- C 22
- D 1
Answer & Solution
Correct Answer
(C) 22
Step-by-step Solution
Detailed explanation
The property of combinations states that if \(^{n}C_{a} = ^{n}C_{b}\), then either \(a = b\) or \(a + b = n\). Given \(^{n}C_{10} = ^{n}C_{12}\), since \(10 \neq 12\), it must be that \(10 + 12 = n\). Therefore, \(n = 22\). We are asked to find \(^{n}C_{21}\), which is…
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