Question

In how many ways can a football team of 11 players be selected from 16 players? How many of these will
(i) include 2 particular players?
(ii) exclude 2 particular players?

Answer 1

Number of ways in which 11 players can be selected out of 16 = ${}^{16}{C}_{11}=\frac{16!}{11!5!}=\frac{16\times 15\times 14\times 13\times 12}{5\times 4\times 3\times 2\times 1}=4368$
(i) If 2 particular players are included, it would mean that out of 14 players, 9 players are selected.
Required number of ways = ${}^{14}{C}_9=\frac{14!}{9!5!}=\frac{14\times 13\times 12\times 11\times 10}{5\times 4\times 3\times 2\times 1}=2002$

(ii) If 2 particular players are excluded, it would mean that out of 14 players, 11 players are selected.
Required number of ways = ${}^{14}{C}_{11}=\frac{14!}{11!3!}=\frac{14\times 13\times 12}{3\times 2\times 1}=364$