JEE Main 2025 — Permutation Combination Question with Solution
JEE Main 2025 (7 Apr Shift 1)
Question
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
Choose an option
Show full solutionCorrect option: B
Correct answer
B155
Step-by-step explanation
7 Batsmen \& 6 Bowlers
To select 10 players including atleast
4 Batsmen \& 4 Bowlers
Captain \& vice-captain already selected
$\begin{aligned}
& \text { No. of ways }={ }^6 \mathrm{C}_5 \times{ }^5 \mathrm{C}_3+{ }^6 \mathrm{C}_4 \times{ }^5 \mathrm{C}_4+{ }^6 \mathrm{C}_3 \times{ }^5 \mathrm{C}_5 \\ & =6 \times 10+15 \times 5+20 \times 1 \\ & =60+75+20=155
\end{aligned}$
To select 10 players including atleast
4 Batsmen \& 4 Bowlers
Captain \& vice-captain already selected
$\begin{aligned}
& \text { No. of ways }={ }^6 \mathrm{C}_5 \times{ }^5 \mathrm{C}_3+{ }^6 \mathrm{C}_4 \times{ }^5 \mathrm{C}_4+{ }^6 \mathrm{C}_3 \times{ }^5 \mathrm{C}_5 \\ & =6 \times 10+15 \times 5+20 \times 1 \\ & =60+75+20=155
\end{aligned}$
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This is a previous-year question from JEE Main 2025, covering the Permutation Combination chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.