Question

I need help with (ii) both (a) and (b) thanks

Answer 1

(i) 126 ways

(ii)

(a) 1/126

(b) 5/14

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

1. 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