Combinations Selection
From a group of 7 men and 6 women, the number of ways to form a committee consisting of exactly 3 men and 2 women, with no further restriction, equals which value?
Select the correct option:
🔒 Solution Hidden from View
Submit your answer to unlock the detailed step-by-step solution.
More permutations and combinations Practice Questions
The number of ways to arrange 4 boys and 4 girls in a row so that no two girls are adjacent to each ...
The number of ways to arrange 4 boys and 4 girls in a row so that no two girls are adjacent to each ...
The number of ways to place 5 distinct letters into 3 distinct mailboxes, where any mailbox may rece...
The number of ways to place 5 distinct letters into 3 distinct mailboxes, where any mailbox may rece...
Given 10 points in a plane of which no three are collinear, the number of distinct triangles that ca...
Given 10 points in a plane of which no three are collinear, the number of distinct triangles that ca...
If the combinatorial equation C(n, 2) equals 28 holds for a positive integer n, then the value of n ...
If the combinatorial equation C(n, 2) equals 28 holds for a positive integer n, then the value of n ...
Using the standard combinatorial identity, the value of the sum C(8,0) + C(8,1) + C(8,2) + ... + C(8...
Using the standard combinatorial identity, the value of the sum C(8,0) + C(8,1) + C(8,2) + ... + C(8...
From 20 points placed on a straight line, the number of line segments that can be formed by joining ...
From 20 points placed on a straight line, the number of line segments that can be formed by joining ...
Using all five digits 1, 2, 3, 4 and 5 exactly once to form five-digit numbers, the sum of all such ...
Using all five digits 1, 2, 3, 4 and 5 exactly once to form five-digit numbers, the sum of all such ...
If all the distinct arrangements of the letters of the word RANK are listed in dictionary order, the...
If all the distinct arrangements of the letters of the word RANK are listed in dictionary order, the...
At a party every pair of guests shakes hands exactly once, and the total number of handshakes record...
At a party every pair of guests shakes hands exactly once, and the total number of handshakes record...
The number of ways to arrange 5 boys and 3 girls in a row so that all 3 girls always stand together ...
The number of ways to arrange 5 boys and 3 girls in a row so that all 3 girls always stand together ...
A student must travel from city A to city C passing through city B, with 4 roads from A to B and 5 r...
A student must travel from city A to city C passing through city B, with 4 roads from A to B and 5 r...
The number of ways to arrange the letters of the word MONDAY so that all the vowels occupy only the ...
The number of ways to arrange the letters of the word MONDAY so that all the vowels occupy only the ...
About This Question
- Subject
- mathematics
- Chapter
- permutations and combinations
- Topic
- combinations selection
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
525
Selecting a committee where order does not matter uses combinations, and independent group selections multiply, a routine JEE Advanced setup. Choosing 3 men from 7 is C(7,3) = 35, and choosing 2 women from 6 is C(6,2) = 15. Since the two selections are independent, the total number of committees is the product 35 × 15 = 525. Order within the committee is irrelevant, which is precisely why combinations rather than permutations are used. Option 210 = C(7,3) × C(6,1) miscounts the women selection. Option 1287 = C(13,5) ignores the gender split entirely. Option 35 counts only the men's selection. Hence there are 525 committees. Plausibility check: each of the 35 ways to pick men pairs with each of the 15 ways to pick women, forming a 35 by 15 grid of committees totalling 525, consistent with the product rule for independent selections.
This easy difficulty mathematics question is from the chapter permutations and combinations, covering the topic of combinations selection. It appeared in the 2025 exam.
Looking for more practice? Explore all mathematics questions or browse permutations and combinations questions on RankGuru.