JEE Mains · Maths · STD 11 - 6. permutation and combination
If \({ }^{n} P_{r}={ }^{n} P_{r+1}\) and \({ }^{n} C_{r}={ }^{n} C_{r-1}\), then the value of \(r\) is equal to:
- A \(3\)
- B \(1\)
- C \(4\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
\({ }^{n} \mathrm{p}_{r}={ }^{n} p_{r+1} \Rightarrow \frac{n !}{(n-r) !}=\frac{n !}{(n-r-1) !}\) \(\Rightarrow(n-r)=1\) \({ }^{n} \mathrm{C}_{\mathrm{r}}={ }^{n} C_{\mathrm{r}-1}\) \(\Rightarrow \frac{n !}{r !(n-r) !}=\frac{n !}{(r-1) !(n-r+1) !}\)…
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