If ^nC_r = 84,^nC_{r-1} = 36,and ^nC_{r+1} = | vedclass

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

Question

(B) We are given the following combinations:$1$) $\frac{^nC_r}{^nC_{r-1}} = \frac{84}{36} = \frac{7}{3}$Using the formula $\frac{^nC_r}{^nC_{r-1}} = \

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(B) We are given the following combinations:$1$) $\frac{^nC_r}{^nC_{r-1}} = \frac{84}{36} = \frac{7}{3}$Using the formula $\frac{^nC_r}{^nC_{r-1}} = \frac{n-r+1}{r}$,we get $\frac{n-r+1}{r} = \frac{7}{3} \implies 3n - 3r + 3 = 7r \implies 3n - 10r = -3$  (Equation $1$)$2$) $\frac{^nC_{r+1}}{^nC_r} = \frac{126}{84} = \frac{3}{2}$Using the formula $\frac{^nC_{r+1}}{^nC_r} = \frac{n-r}{r+1}$,we get $\frac{n-r}{r+1} = \frac{3}{2} \implies 2n - 2r = 3r + 3 \implies 2n - 5r = 3$ (Equation $2$)Multiply Equation $2$ by $2$: $4n - 10r = 6$ (Equation $3$)Subtract Equation $1$ from Equation $3$: $(4n - 10r) - (3n - 10r) = 6 - (-3) \implies n = 9$.Substituting $n=9$ into Equation $2$: $2(9) - 5r = 3 \implies 18 - 5r = 3 \implies 5r = 15 \implies r = 3$.

If $^nC_r = 84$,$^nC_{r-1} = 36$,and $^nC_{r+1} = 126$,then $n$ equals:

Similar Questions

$6$ points in a plane are joined in all possible ways by indefinite straight lines. If no two lines are coincident or parallel,and no three lines pass through the same point (with the exception of the original $6$ points),the number of distinct points of intersection is equal to

It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?

The Chief Ministers of $11$ States of India meet to discuss the language problem. In how many ways can they seat themselves at a round table so that the Punjab and Madras Chief Ministers sit together?

In how many ways can $10$ balls be divided between two boys,if one receives two balls and the other receives eight balls?

How many numbers of four digits can be formed with the digits $1, 2, 3, 4$ and $5$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module