From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be included. Then th

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Solution

Q.
From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is [2025]

1 145

2 155

3 165

4 135

Ans.
(2)

To select 10 players including atleast 4 batsmen and 4 bowlers.

Captain and vice-captain already selected

$∴$ Total number of ways = ${}^{6}C_{5} \times {}^{5}C_{3} + {}^{6}C_{4} \times {}^{5}C_{4} + {}^{6}C_{3} \times {}^{5}C_{5}$

= $6 \times 10 + 15 \times 5 + 20 \times 1$

= 60 + 75 + 20 = 155

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