Find the number of different arrangements of the books if there are no restrictions.

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

1. [B1] 40320
2. [B1] No. of ways with maths books as 1 unit = 5! or 5×4! or ⁵P₅ or 120
3. [B1] No. of ways maths books can be arranged amongst themselves = 4! or ⁴P₄ or 24
4. [B1] Total = (5! ×4! oe) = 2880
5. [B1] No. of ways with maths books as 1 unit and geography books as 1 unit = 3! or ³P₃ or 3×2! or 6
6. [B1] No. of ways maths books can be arranged amongst themselves and geography books can be arranged amongst themselves = 4! ×3! or ⁴P₄ x ³P₃ or 144
7. [B1] Total = (3! ×4! ×3! oe) = 864
8. [B1] ¹²C₆ = 924
9. [M1] Either: 924 – ⁸C₆ For their (i) – the number of teams of just men
10. [A1] Total = 896
11. [M1] Or: 5M 1W : ⁸C₅ × ⁴C₁ (=224) 4M 2W : ⁸C₄ x ⁴C₂ (= 420) 3M 3W : ⁸C₃ × ⁴C₃ (= 224) 2M 4W : ⁸C₂x⁴C₄ (= 28) For a complete method
12. [A1] Total = 896