The difference between the maximum value of { | vedclass

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

Question

(D) The maximum value of ${}^6C_r$ occurs at $r = \frac{6}{2} = 3$. The value is ${}^6C_3 = \frac{6!}{3!3!} = \frac{6 	imes 5 	imes 4}{3 	imes 2

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) The maximum value of ${}^6C_r$ occurs at $r = \frac{6}{2} = 3$. The value is ${}^6C_3 = \frac{6!}{3!3!} = \frac{6 	imes 5 	imes 4}{3 	imes 2 	imes 1} = 20$. Given that the difference between the maximum value of ${}^6C_r$ and ${}^nC_3$ is $16$,we have $|20 - {}^nC_3| = 16$. This implies ${}^nC_3 = 20 + 16 = 36$ or ${}^nC_3 = 20 - 16 = 4$. Case $1$: ${}^nC_3 = 36$ $\Rightarrow \frac{n(n-1)(n-2)}{6} = 36$ $\Rightarrow n(n-1)(n-2) = 216$. There is no integer $n$ satisfying this. Case $2$: ${}^nC_3 = 4$ $\Rightarrow \frac{n(n-1)(n-2)}{6} = 4$ $\Rightarrow n(n-1)(n-2) = 24$. Testing values,for $n=4$,$4 	imes 3 	imes 2 = 24$. Thus,$n = 4$.

The difference between the maximum value of ${}^6C_r$ and ${}^nC_3$ is $16$. Then $n=$

Similar Questions

The least value of the natural number $n$ satisfying $C(n, 5)+C(n, 6)>C(n+1, 5)$ is

$\binom{15}{8} + \binom{15}{9} - \binom{15}{6} - \binom{15}{7} = \dots$

If $^nC_{r-2} = 36$,$^nC_{r-1} = 84$,and $^nC_r = 126$,then the value of $^nC_{2r}$ is

$A$ committee of $7$ members is to be formed from $9$ boys and $4$ girls. In how many ways can this be done if the committee must consist of at least $3$ girls?

$A$ father with $8$ children takes them $3$ at a time to the Zoological gardens,as often as he can without taking the same $3$ children together more than once. The number of times each child will go to the garden is

Vedclass Test Series

Exam Paper Generator

Online Exam Module