Quantitative Reasoning

Permutation & Combination

Medium

The number of ways a committee consisting of 3 men and 1 women can be formed from 5 men and 3 women, is _________ .

✅ Correct Option: 2

A committee consisting of 3 men and 1 woman needs to be formed from 5 men and 3 women.

The number of ways to select 3 men from 5 men:

$^5C_3 = \dfrac{5!}{3! \times 2!}$

$= \dfrac{5 \times 4 \times 3!}{3! \times 2 \times 1}$

$= \dfrac{5 \times 4}{2 \times 1}$

$= \dfrac{20}{2}$

$= 10$

The number of ways to select 1 woman from 3 women:

$^3C_1 = \dfrac{3!}{1! \times 2!}$

$= 3$

Since both selections must be made together to form the committee, the results are multiplied:

Total number of ways $= 10 \times 3$

$= 30$

Therefore, the number of ways to form the committee is 30.

2025: 20 May Shift 2

Match List-I with List-II

List-I	List-II
(Expressions)	(Values)
(A) 1/6! + 1/7! = x/8! Find x	(I) 1
(B) Evaluate: $\frac{n!}{(n-r)!}$ , n = 6, r = 2	(II) 100
(C) If ⁿC₉ = ⁿC₈, find ⁿC₁₇.	(III) 64
(D) ⁶P₃ - ⁵P₂	(IV) 30

Choose the correct answer from the options given below:

2026: 19 May Shift 2

A committee of 5 members is to be formed by selecting out of 6 men and 4 women. In how many different ways the committee can be formed if it should have at least 2 women?

2025: 15 May Shift 1

Read the information given below carefully and answer the question that follows:

(A) The different ways in which the alphabets of the word BAKERY can be arranged is 720

(B) The number of ways in which the alphabets of the word MACHINE can be arranged so that the vowels will occupy only the odd positions is 576

Choose the correct answer from the options given below:

2025: 24 May Shift 2

In a plane, there are 9 points, out of which 4 are collinear. The number of triangles made by these points is:

2025: 15 May Shift 1

Five digit numbers formed by using digits 0, 1, 2, 3 and 4 (when repitition of digits are not allowed) are:

2025: 30 May Shift 2

In how many different ways can the letters of the word 'DELETE' be arranged?

The number of ways a committee consisting of 3 men and 1 women can be formed from 5 men and 3 women, is _________ .

Solution

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