In how many ways can a cricket team be selected from a group of 25 players containing 10 batsmen, 8 bowlers, 5 all-rounders and 2 wicketkeepers, assuming that the team of 11 players requires 5 batsmen, 3 all-rounders, 2 bowlers and 1 wicketkeeper?

Answer : A team of 11 players is to be made from 25 players.

⇒ Selecting 5 batsmen from 10 in ¹⁰C5 ways.

⇒ Selecting 3 all-rounders from 5 in ⁵C3 ways.

⇒ Selecting 2 bowlers from 8 in ⁸C2 ways.

⇒ Selecting 1 wicketkeeper from 2 in ²C1 ways. Thus, by the multiplication principle, we get

= 10C5      8C2      5C3      2C1 ways

Applying ⁿCr =

= 141120 ways