## Part (i)

**Answer:** $\binom{11}{3} = 165$

| **Marks** | **Guidance** |
|-----------|--------------|
| M1 | Seen |
| A1 | cao |
| **[2]** | |

## Part (ii)

**Answer:** $\frac{\binom{5}{2} \times \binom{6}{1}}{\binom{11}{3}} + \frac{\binom{5}{3} \times \binom{6}{0}}{\binom{11}{3}} = \frac{60}{165} + \frac{10}{165} = \frac{70}{165} = \frac{14}{33} = 0.424$

**Alternative:**
$1 - P(1 \text{ or } 0) = 1 - 3 \times \frac{5}{11} \times \frac{10}{9} \times \frac{5}{9} \times \frac{6}{10} \times \frac{5}{11} \times \frac{4}{9}$

$= 1 - \frac{5}{11} - \frac{4}{33} = \frac{14}{33}$

M1 for $1 - P(1 \text{ or } 0)$, M1 for first product, M1 for second product, A1

| **Marks** | **Guidance** |
|-----------|--------------|
| M1 | For intention to add correct two fractional terms |
| M1 | For numerator of first term |
| M1 | For numerator of sec term. Do not penalise omission of $\binom{6}{0}$ |
| M1 | For correct denominator |
| A1 | cao |
| **[5]** | Or. For attempt at correct two terms. For prod of 3 correct fractions $=4/33$. For whole expression ie $3 \times \frac{5}{11} \times \frac{10}{9} \times \frac{6}{11} \left(\frac{-4}{11}\right) (= 3 \times 0.1212\ldots)$ |

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