Search any question & find its solution
Question:
Answered & Verified by Expert
If \({ }^n P_r={ }^n P_{r+1}\) and \({ }^n C_r={ }^n C_{r-1}\), then the values of \(\mathrm{n}\) and \(\mathrm{r}\) are
Options:
Solution:
1146 Upvotes
Verified Answer
The correct answer is:
3,2
We have, \({ }^n P_r={ }^n P_{r+1}\)
\(\begin{aligned}
& \Rightarrow \frac{n !}{(n-r) !}=\frac{n !}{(n-r-1) !} \Rightarrow \frac{1}{(n-r)}=1 \\
& \text { or } n-r=1 \\
& \text { Also, }{ }^n C_r={ }^n C_{r-1} \Rightarrow r+r-1=n \\
& \Rightarrow 2 r-n=1
\end{aligned}\)
Solving (1) and (2), we get \(r=2\) and \(n=3\)
\(\begin{aligned}
& \Rightarrow \frac{n !}{(n-r) !}=\frac{n !}{(n-r-1) !} \Rightarrow \frac{1}{(n-r)}=1 \\
& \text { or } n-r=1 \\
& \text { Also, }{ }^n C_r={ }^n C_{r-1} \Rightarrow r+r-1=n \\
& \Rightarrow 2 r-n=1
\end{aligned}\)
Solving (1) and (2), we get \(r=2\) and \(n=3\)
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.