Question #5
Choose the best option
There are 18 players including 2 wicket-keepers and 5 bowlers, available for selecting a
Cricket team of 11 players. In how many ways can a team of 11 players be selected if we have
to select 1 wicket-keeper and at least 4 bowlers?
3654
4684
5544
6124
Answers
Given : There are 18 players including 2 wicket-keepers and 5 bowlers, available for selecting a Cricket team of 11 players.
we have to select 1 wicket-keeper and at least 4 bowlers?
To Find : Number of ways
3654
4684
5544
6124
Solution:
18 player
Wicket keepers = 2
Bowlers = 5
Other players = 11
1 wicket keeper out of 2 can be selected in 2 ways
Bowlers can be selected wither 4 or 5
Then other players selected = 6 or 5
4 bowlers selected the ⁵C₄ * ¹¹C₆ = 5 * 462
5 bowlers selected the ⁵C₅ * ¹¹C₅ = 1 * 462
Hence Total ways = 2 ( 5 * 462 + 1 * 462)
= 2 * 6 * 462
= 5544 ways
in 5544 ways team can be selected if we have to select 1 wicket-keeper and at least 4 bowlers
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