Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20257 AprilMorning Shift
Exam
JEE Main
Year
2025
Date
7 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2025 · 7 April · Morning Shift · Mathematics · Permutation and Combination

From a group of 7 batsmen and 6 bowlers, 10 players are to be...

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

Options

  1. A165
  2. B155
  3. C145
  4. D135

Correct answer

B. 155

Step-by-step solution

7 Batsmen \& 6 BowlersTo select 10 players including atleast4 Batsmen \& 4 BowlersCaptain \& vice-captain already selected No. of ways =6C5×5C3+6C4×5C4+6C3×5C5=6×10+15×5+20×1=60+75+20=155\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}
Practice Permutation and Combination on Quantrex Academy →

More from Permutation and Combination

All Permutation and Combination questions Full Permutation and Combination list Permutation and Combination JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs