Question

A cricket 11 is to be chosen from 16 players of whom 7 are bowlers, 4 can keep the wicket. Number o

ways this can be done to contain exactly 5 bowlers, 2 wicketkeepers is
1) 945
2) 885
3) 630
4) 715

Answer 1

Answer:630

Explanation:

• We have to pick 11 players including 5 bowlers and 2 keepers
• The number of ways in which we can choose 5 bowlers out of 7 are 7C5 = 7!/(5!*2!) =21
• The no. of ways in which 2 keepers can be selected out of 4 are 4C2 = 4!/(2!*2!) =6
• The number of ways to select remaining (11-5-2=) 4 players out of remaining (16-7-4=) 5 players are 5C4 = 5! /(4!*1!) = 5
• So, the total number of ways to select the team of 11 is 21 * 6 * 5 = 630