Answer:
(a) 2 white & 1 red ball = 42 ways
(b) All 3 white balls = 4 ways
(c) All 3 red balls = 35 ways
Explanation:
An urn contains 4 white balls and 7 red balls. Three balls are selected.
In how many ways can the 3 balls be drawn from a total of 11 balls:
(a) If 2 balls are white and 1 is red?
The 2 white balls can be selected in ⁴C₂ ways
The 1 red ball can be selected in ⁷C₁ ways
2 white & 1 red ball = ⁴C₂ × ⁷C₁
2 white & 1 red ball = 6 × 7
2 white & 1 red ball = 42 ways
(b) If all 3 balls are white?
The 3 white balls can be selected in ⁴C₃ ways
The 0 red ball can be selected in ⁷C₀ ways
All 3 white balls = ⁴C₃ × ⁷C₀
All 3 white balls = 4 × 1
All 3 white balls = 4 ways
(c) If all 3 balls are red?
The 3 red balls can be selected in ⁷C₃ ways
The 0 white ball can be selected in ⁴C₀ ways
All 3 red balls = ⁷C₃ × ⁴C₀
All 3 red balls = 35 × 1
All 3 red balls = 35 ways