CUET UG 2025 — General Test Quantitative Reasoning

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:

$$^5C_3 = \dfrac{5!}{3! \times 2!}$$5C3​=3!×2!5!​

$$= \dfrac{5 \times 4 \times 3!}{3! \times 2 \times 1}$$=3!×2×15×4×3!​

$$= \dfrac{5 \times 4}{2 \times 1}$$=2×15×4​

$$= \dfrac{20}{2}$$=220​

$$= 10$$=10

---

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

$$^3C_1 = \dfrac{3!}{1! \times 2!}$$3C1​=1!×2!3!​

$$= 3$$=3

---

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

Total number of ways $= 10 \times 3$=10×3

$$= 30$$=30

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