The value of frac{{}^{10}C_{r}}{{}^{11}C_{r}} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The greatest value of ${}^{n}C_{r}$ occurs at $r = \frac{n}{2}$ if $n$ is even,and at $r = \frac{n-1}{2}$ or $r = \frac{n+1}{2}$ if $n$ is odd.For

Vedclass · Accepted Answer

$\frac{6}{11}$

Vedclass · Answer

(A) The greatest value of ${}^{n}C_{r}$ occurs at $r = \frac{n}{2}$ if $n$ is even,and at $r = \frac{n-1}{2}$ or $r = \frac{n+1}{2}$ if $n$ is odd.For ${}^{10}C_{r}$,$n=10$ (even),so the greatest value is at $r = \frac{10}{2} = 5$.For ${}^{11}C_{r}$,$n=11$ (odd),so the greatest values are at $r = \frac{11-1}{2} = 5$ and $r = \frac{11+1}{2} = 6$.Taking $r=5$ for both,we have:$\frac{{}^{10}C_{5}}{{}^{11}C_{5}} = \frac{\frac{10!}{5!5!}}{\frac{11!}{5!6!}} = \frac{10!}{5!5!} 	imes \frac{5!6!}{11!} = \frac{10!}{11!} 	imes \frac{6!}{5!} = \frac{1}{11} 	imes 6 = \frac{6}{11}$.

The value of $\frac{{}^{10}C_{r}}{{}^{11}C_{r}}$,when both the numerator and denominator are at their greatest values,is

Similar Questions

If the domain and range of $f(x) = ^{9-x}C_{x-1}$ contain $m$ and $n$ elements respectively,then:

$A$ committee of $5$ is to be formed out of $6$ men and $4$ ladies. The number of ways this can be done,when at most $2$ ladies are included,is

The greatest positive integer which divides $(n+16)(n+17)(n+18)(n+19)$,for all positive integers $n$,is

If ${ }^9 C_3+{ }^9 C_5={ }^{10} C_r$ for some $r \in N$,then $r=$

Sangeeta plans a dinner party for $6$ guests. Out of $10$ friends,in how many ways can she choose the guests if two specific friends cannot attend the party together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module