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
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.
🔒 Solution Hidden from View
Submit your answer to unlock the detailed step-by-step solution.
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.