Question

A team of 11 is to be chosen from 18 cricketers of whom 6 are bowlers and 3 are wicket keepers. In how many ways can a team be chosen so that. 

i. There are exactly 4 bowlers and one wicket keeper 

ii. There are at least 4 bowlers and at least 2 wicket keepers.

Answer 1

Bowlers(6)	Wicket keeper (3)	Others (9)	Number of selection
4	1	6	6C43C19C6 = 3780
4	2	5	6C43C29C5 = 5670
4	3	4	6C43C19C4 = 1890
5	2	4	6C53C29C3 = 2268
5	3	3	6C53C29C3 = 504
6	2	3	6C63C29C3 = 252
6	3	2	6C63C39C2 = 36
Total			= 14364