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 relations for combinations:$1$) $\frac{^nC_r}{^nC_{r-1}} = \frac{n-r+1}{r} = \frac{84}{36} = \frac{7}{3}$$2$) $\frac{^n

Vedclass · Accepted Answer

$9$

Vedclass · Answer

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

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

Similar Questions

In how many ways can a committee be formed of $5$ members from $6$ men and $4$ women if the committee has at least one woman?

The number of $4$-digit numbers without repetition that can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ in which each number has two odd digits and two even digits is:

If ${ }^{n+4} C_{n+1}-{ }^{n+3} C_n=15(n+2)$,then $n=$

$_n{P_r} \div \binom{n}{r} = ..........$

The number of ways in which a committee of $6$ members can be formed from $8$ gentlemen and $4$ ladies so that the committee contains at least $3$ ladies is

Vedclass Test Series

Exam Paper Generator

Online Exam Module