JEE Mains · Maths · STD 11 - 6. permutation and combination
The value of \(r\) for which \(^{20}{C_r}^{20}{C_0}{ + ^{20}}{C_{r - 1}}^{20}{C_1}{ + ^{20}}{C_{r - 2}}^{20}{C_2} + ...{ + ^{20}}{C_0}^{20}{C_r}\) is maximum is
- A \(15\)
- B \(20\)
- C \(11\)
- D \(10\)
Answer & Solution
Correct Answer
(B) \(20\)
Step-by-step Solution
Detailed explanation
\(^{20}{C_r}{.^{20}}{C_0}{ + ^{20}}{C_{r - 1}}{.^{20}}{C_1} + ......{ + ^{20}}{C_0}{.^{20}}{C_r} = \) Selecting \(r\) student from \(20\) boys and \(20\) girls \({ = ^{40}}{C_r}\) \(^{40}{C_r}\) will be maximum if \(r=20.\)
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