Question

For the post or 5 teachers there are 23 applicants 2 posts are reserved for sc candidates and there are 7 sc candidates among the applicants in how many ways can the selection be made

Answer 1

$\sf{\underline{Answer:}}$

In 11760 ways, the selection can be made.

$\sf{\underline{Given:}}$

Total applicants = 23

No. of SC candidates = 7

Remaining no. of candidates = 23 - 7 = 16

$\sf{\underline{We\:know\:that:}}$

2 seats are reserved for SC candidates.

No. of ways of forming groups = $\boxed{\sf{^{7}C_{2}}}$

$\sf{\underline{And:}}$

Remaining candidates = $\boxed{\sf{^{16}C_{3}}}$

Total no. of ways of selecting 5 teachers:

$\boxed{\sf{^{16}C_{3}\times ^{7}C_{2}}}$

$\sf{\underline{Now:}}$

$^{16}C_{3} \times ^{7}C_{2}$

$= \frac{16!}{3! (16 - 3)!} \times \frac{7!}{2! (7 - 2)!}$

$= \frac{16!}{3!\:13!} \times \frac{7!}{2!\:5!}$

$= \frac{16 \times 15 \times 14 }{3 \times 2 \times 1} \times \frac{7 \times 6}{2 \times 1}$

$=\frac{3360}{6} \times \frac{42}{2}$

$= 560 \times 21$

$=\boxed{ 11760}$

$\sf{\underline{Therefore:}}$

In 11760 ways, the selection can be made.