**(i)** $\frac{7!}{2!} = 2520$ | M1, A1 2 | For dividing by 2 or 2!; For correct answer

**(ii)** $\frac{5!}{2!} \times 3! = 360$ | B1, M1 | For 5! or equivalent; For multiplying by 3! or dividing by 2! or both

| A1 3 | For correct answer

**(iii)** $\frac{4}{7} \text{ of } 2520 = 1440$ | M2, A1 | For 4/7 of their (i); For correct answer

OR $6! \cdot \frac{6}{2} \cdot \frac{6}{2} = 1440$ | M1, A1, A1 3 | For summing options for ending in 2, 6, 8; For correct options; For correct answer

**(ii) (i)** $\mu = 3.6$ | B1 | Stated or can be calculated later on

$\frac{2.8 - (\text{their}\mu)}{\sigma} = -0.4$ | M1 | For equation relating $\mu$ or 3.6 and $\sigma$. Must be standardised, can have ±0.4

$\sigma = 2$ | M1 | Solving the correct equation or with a second correct equation relating $\mu$ and $\sigma$

| A1 4 | For correct answer

**$(0.6554)^4 \times (0.3446)^3 \times _4C_3 + (0.6554)^3 \times (0.3446)^4 \times _4C_3 = 0.879$ (= 0.3061 +0.3881 +0.1845) | M1, B1, A1, A1 | For attempted binomial calculation of any 2 or 3 of P(2), P(3), P(4), needs 0.6554 in; For correct numerical expression for P(2) or P(3); All in correct form; For correct answer

OR $1 - (0.3446)^4 - (0.6554)^4 \times (0.3446)^3 \times _4C_3 (= 1 - 0.0141 - 0.1072) = 0.879$ | M1, B1, A1, A1 4 | For calculation of 1 – any 2 or 3 of P(0), P(1), P(2); For correct numerical expression for P(1) or P(2); All in correct form; For correct answer