The Indian cricket team consist of 16 players. It includes 2 wicket keepers and 5 bowlers. In how many ways eleven player can be selected if we have to select on wicket keeper and at-least 4 bowlers?
Question
The Indian cricket team consist of 16 players. It includes 2 wicket keepers and 5 bowlers. In how many ways eleven player can be selected if we have to select on wicket keeper and at-least 4 bowlers?
Solution
To solve this problem, we need to use the concept of combinations from combinatorics. Here are the steps:
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We have 16 players in total: 2 wicket keepers and 14 other players (5 of whom are bowlers).
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We need to select 1 wicket keeper. This can be done in 2C1 ways (which is 2).
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We need to select at least 4 bowlers. This can be done in the following ways:
- Select 4 bowlers and 6 other players: This can be done in 5C4 * 9C6 ways.
- Select 5 bowlers and 5 other players: This can be done in 5C5 * 9C5 ways.
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Add the two cases to get the total number of ways.
So, the total number of ways to select the team is:
= 2C1 * [ (5C4 * 9C6) + (5C5 * 9C5) ]
= 2 * [ (5 * 84) + (1 * 126) ]
= 2 * [ 420 + 126 ]
= 2 * 546
= 1092
So, the Indian cricket team can be selected in 1092 ways.
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