**(a)**

e.g. P*N*P*P*L

M1 | Multiply by $5!$ in numerator

$\frac{5!}{3! \cdot 2!} \times 6P_4 = 3600$

M1 | Divide by $3!$ or $2!$

M1 | Multiply by $6P_4$ or equivalent

A1 | [4]

**(b) (i)**

$\binom{7}{5} \times \binom{5}{4} \times \binom{2}{1} \times \binom{2}{1} = 420$

M1 | Multiply 4 combinations of which three are correct

A1 | [2]

**(ii)**

Both in team: $\binom{6}{4} \times \binom{4}{3} \times 2 \times 2 = 240$

M1 | Evaluating both in team and subtracting from (i)

$420 - 240 = 180$ ways

M1 | Follow-through their 420, their 240

A1 | [3]

**OR**

Bat in bowl out + bowl in bat out + both out

$= \binom{6}{4} \times \binom{4}{3} \times 2 \times 2 + \binom{6}{5} \times \binom{4}{3} \times 2 \times 2 + \binom{6}{5} \times \binom{4}{4} \times 2 \times 2$

$= 60 + 96 + 24 = 180$ ways

M1 | Summing 2 or 3 options not both in team

A1 | 2 or 3 options correct, unsimplified

A1 | Correct answer from correct working

**OR**

Bat in bowl out + bat out

$= 60 + \binom{6}{5} \times \binom{5}{4} \times 2 \times 2 = 60 + 120 = 180$ ways

M1 | As above, or bowl in bat out + bowl out

A1 A1 | [3]

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