WBJEE · Maths · Permutation Combination
If \({ }^9 P_5+5 .{ }^9 P_4={ }^{10} P_r\), then the value ' \(r\) ' is
- A \(4\)
- B \(8\)
- C \(5\)
- D \(7\)
Answer & Solution
Correct Answer
(C) \(5\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned}{ }^9 P_5+5. ^9P_4 & =\frac{9!}{4!}+5 \cdot \frac{9!}{5!} \\ & =\frac{9!}{4!}+\frac{9!}{4!}=2 \cdot \frac{9!}{4!} \\ & =2 \cdot \frac{10.9!}{10.4!}=\frac{10!}{5!}={ }^{10} P_r \\ & \Rightarrow r=5\end{aligned}\)
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