Answer:
(i) 126 ways
(ii)
(a) 1/126
(b) 5/14
Step-by-step explanation:
(i) Possible selections
- ⁹C₄ = 9! / 5! 4!
- 9 x 8 x 7 x 6 x 5! / 5! x 4 x 3 x 2 x 1
- 72 x 7 x 6 / 24
- 7 x 6 x 3
- 42 x 3
- 126 ways
(ii) (a) all girls
- ⁴C₄
- 4! / 1! 4!
- 1 way
- P = 1/126
(ii) (b) more boys than girls
- 3 boys, 1 girl
- ⁵C₃ x ⁴C₁
- (5! / 2! 3!) x (4! / 3! 1!)
- (5 x 4 x 3!/ 2 x 3!) x (4 x 3! / 3!)
- 10 x 4
- 40 ways
2. 4 boys, no girls
- ⁵C₄
- 5! / 1! 4!
- 5 x 4! / 4!
- 5 ways
⇒ 40 + 5 = 45 ways
⇒ P = 45/126 = 15/42 = 5/14
