First slide

Combinations

Question

If $^{n} C_{r - 1} = 36,^{n} C_{r} = 84 {and}^{n} C_{r + 1} = 126,$ then the value of $r$ is equal to

Moderate

A

1
B

2
C

3
D

4

Solution

We have
$\frac{^{n} C_{r - 1}}{^{n} C_{r}} = \frac{36}{84} \Rightarrow \frac{n!}{(r - 1)! (n - r + 1)!} \frac{r! (n - r)!}{n!} = \frac{3}{7}$
$\Rightarrow \frac{r}{n - r + 1} = \frac{3}{7} \Rightarrow 10 r = 3 n + 3$
Similarly $\frac{^{n} C_{r}}{^{n} C_{r + 1}} = \frac{84}{126} \Rightarrow \frac{r + 1}{n - r} = \frac{2}{3}$
$\Rightarrow 5 r + 3 = 2 n \Rightarrow 5 r + 3 = 2 n$
Solving we obtain $r$ = 3.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App