Determine n if ^{2n}C_{3} : ^{n}C_{3} = 12 : | vedclass

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

Question

(A) Given $\frac{^{2n}C_{3}}{^{n}C_{3}} = \frac{12}{1}$.Using the formula $^{n}C_{r} = \frac{n!}{r!(n-r)!}$,we have:$\frac{(2n)!}{3!(2n-3)!} 	imes \f

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(A) Given $\frac{^{2n}C_{3}}{^{n}C_{3}} = \frac{12}{1}$.Using the formula $^{n}C_{r} = \frac{n!}{r!(n-r)!}$,we have:$\frac{(2n)!}{3!(2n-3)!} 	imes \frac{3!(n-3)!}{n!} = 12$.Simplifying the factorials:$\frac{(2n)(2n-1)(2n-2)(2n-3)!}{(2n-3)!} 	imes \frac{(n-3)!}{n(n-1)(n-2)(n-3)!} = 12$.$\frac{(2n)(2n-1)(2(n-1))}{n(n-1)(n-2)} = 12$.$\frac{2(2n-1)(2)}{n-2} = 12$.$\frac{4(2n-1)}{n-2} = 12$.$\frac{2n-1}{n-2} = 3$.$2n - 1 = 3(n - 2)$.$2n - 1 = 3n - 6$.$n = 5$.

Determine $n$ if $^{2n}C_{3} : ^{n}C_{3} = 12 : 1$.

Similar Questions

$^{20}C_1 + 3 ^{20}C_2 + 3 ^{20}C_3 + ^{20}C_4$ is equal to-

$^nC_r + ^{n-1}C_r + ...... + ^rC_r =$

The number of integers between $100$ and $1000$ such that the sum of their digits is equal to $14$ is:

If $5$ dice are rolled simultaneously,then the number of ways of getting a total of $7$ on their faces is:

The number of ways in which $17$ apples can be distributed among $4$ guests such that each guest gets at least $3$ apples is

Vedclass Test Series

Exam Paper Generator

Online Exam Module