JEE MAIN - Mathematics (2025 - 7th April Morning Shift - No. 1)
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
145
165
155
135
Explanation
1 Captain, 1 vice-captain are already present
$\Rightarrow$ We need to select 8 players such that atleast 3 batsman and bowler must be there
| Batsman | Bowler | Number of ways |
|---|---|---|
| 3 | 5 | ${ }^6 C_3 \cdot{ }^5 C_5=20$ |
| 4 | 4 | ${ }^6 C_4 \cdot{ }^5 C_4=75$ |
| 5 | 3 | ${ }^6 C_5 \cdot{ }^5 C_3=60$ |
Total = 155 ways
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