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In a cricket team, there are 5 bowlers, 2 allrounders and 4 batsmen. In how many ways, a group of 4 players can be formed such that it has 1 bowler, 1 allrounder and 2 batsmen?

In a cricket team, there are 5 bowlers, 2 allrounders and 4 batsmen. In how many ways, a group of 4 players can be formed such that it has 1 bowler, 1 allrounder and 2 batsmen? Correct Answer 60

GIVEN:

In a cricket team, there are 5 bowlers, 2 allrounders and 4 batsmen.

CONCEPT:

Basic concept of Permutation and combination.

Number of ways to select ‘a’ out of ‘b’ = bCa

CALCULATION:

Team contains 5 bowlers, 2 allrounders and 4 batsmen.

We want 1 bowler, 1 allrounder and 2 batsmen

∴ Required number of ways = 5C1 × 2C1 × 4C2

⇒ 5 × 2 × 6

⇒ 60

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