Match List-I with List-II

An urn contains 4 white and 3 red balls. In a random draw of three balls, the probability of

Choose the correct answer from the options given below:

(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

The correct answer is Option (2) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

Total balls = 4 white + 3 red = 7

Total ways to choose 3 balls = 7^C₃ = 35

(A) No red ball ⇒ all 3 white

Ways = 4^C₃ = 4

Probability = \(\frac{4}{35}\) ⇒ (A) → (III)

(B) Only 1 red ball ⇒ 1 red, 2 white

Ways = 3^C₁ × 4^C₂ = 3 × 6 = 18

Probability = \(\frac{18}{35}\) ⇒ (B) → (IV)

(C) Exactly 2 red balls ⇒ 2 red, 1 white

Ways = 3^C₂ × 4^C₁ = 3 × 4 = 12

Probability = \(\frac{12}{35}\) ⇒ (C) → (I)

(D) No white ball ⇒ all 3 red

Ways = 3^C₃ = 1

Probability = \(\frac{1}{35}\) ⇒ (D) → (II)