Jai and his wife Kaz are having a party. Jai has invited five friends and each friend will bring his wife.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

1. [M1] 6! × a, a integer > 1.
2. [M1] b × 2⁶, b integer ≥ 1.
3. [A1] Accurate answer required. SC B1 for 46080 if M0 M0 www.
4. [M1] c × d × e × f × g × h 2 < c, d, e, f, g, h (different integers) < 12.
5. [M1] Correct unsimplified.
6. [A1] Accurate answer required. SC B1 for 46080 if M0 M0 www.
7. [M1] 5! × 5! × k, k positive integer, 1 may be implied (no adding/subtracting).
8. [A1]
9. [B1] Correct probability for one identified scenario. In the group of 5: 5/12 × 4/11 = 20/132 [= 5/33] In the group of 4: 4/12 × 3/11 = 12/132 [= 1/11] In the group of 3: 3/12 × 2/11 = 6/132 [= 1/22]
10. [M1] Denominator 12×11 for all probabilities, (1, 2 or 3 scenarios).
11. [A1] 3 correct probabilities, accept unsimplified.
12. [M1] Adding probabilities for 3 correct scenarios.
13. [A1] 0.2878787 to at least 3SF.
14. [B1] Correct value of one identified scenario seen, accept unsimplified. In the group of 5: ¹⁰C₃ × ⁷C₄ [= 120 × 35 = 4200] In the group of 4: ¹⁰C₂ × ⁸C₅ [= 45 × 56 = 2520] In the group of 3: ¹⁰C₁ × ⁹C₅ [= 10 × 126 = 1260]
15. [M1] ¹²Cₐ × ¹²⁻ᵃCь, a = 3, 4, 5; b = 3, 4, 5 (a ≠ b)
16. [A1] 27720 Seen alone or as denominator of probability - accept unsimplified. SC B1 if M0.
17. [M1] Values of 3 correct scenarios added, accept unsimplified – or correct.
18. [A1] 0.2878787 to at least 3SF.