Mathematics · Permutations and Combinations

JEE Main 2025 — 7 April, Morning Shift — Question 32

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

Option A:
135
Option B:
165
Option C:
145
Option D:
155
Correct

Answer: D

Step-by-step solution

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	${}^6C_3 \cdot {}^5C_5 = 20 \cdot 1 = 20$
4	4	${}^6C_4 \cdot {}^5C_4 = 15 \cdot 5 = 75$
4	3	${}^6C_5 \cdot {}^5C_3 = 6 \cdot 10 = 60$

Total $=155$ ways

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 7 April, Morning Shift
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Applications of Permuations and Combination

The number of singular matrices of order 2, whose elements are from the set \2,3,6,9\ , is \ \ \ \ .

Answer: D

Step-by-step solution

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