If ^{43}{C_{r - 6}} = {,^{43}}{C_{3r + 1}}, then value of r is

English

Gujarati

Hindi

6.Permutation and Combination

easy

If $^{43}{C_{r - 6}} = {\,^{43}}{C_{3r + 1}},$ then the value of $r$ is

A

$12$

B

$8$

C

$6$

D

$10$

Solution

(a) Given, $^{43}{C_{r – 6}}\, = {\,^{43}}{C_{3r + 1}}$

==> $r – 6 = 3r + 1$ or $r – 6 + 3r + 1 = 43$

==> $r = – \frac{7}{2}$ (impossible) or $r = 12$.

Standard 11

Mathematics

Share

Similar Questions

If $^{20}{C_{n + 2}}{ = ^n}{C_{16}}$, then the value of $n$ is

easy

In how many ways $5$ speakers $S_1,S_2,S_3,S_4$ and $S_5$ can give speeches one after the other if $S_3$ wants to speak after $S_1$ & $S_2$

normal

There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84,$ then the value of $m$ is

hard

(JEE MAIN-2019)

The number of $6-$letter words, with or without meaning, that can be formed using the letters of the word $\text{MATHS}$ such that any letter that appears in the word must appear at least twice, is $. . . .. .. $

hard

(JEE MAIN-2025)

How many different words can be formed by jumbling the letters in the word $MISSISSIPPI$ in which no two $S$ are adjacent $?$

hard

(AIEEE-2008)