A-LevelMathematicsProbability and statistics9709/52 · Oct/Nov 2020 · Q611 Marks

Mr and Mrs Ahmed with their two children, and Mr and Mrs Baker with their three children, are visiting an activity centre together. They will divide into groups for some of the activities.

(a)In how many ways can the 9 people be divided into a group of 6 and a group of 3?[2]
(b)5 of the 9 people are selected at random for a particular activity. Find the probability that this group of 5 people contains all 3 of the Baker children.[3]
(c)All 9 people stand in a line. Find the number of different arrangements in which Mr Ahmed is not standing next to Mr Baker.[3]
(d)Find the number of different arrangements in which there is exactly one person between Mr Ahmed and Mr Baker.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[M1] 9Ck × n, k = 6, 3, n = 1,2 oe Condone 9C6 + 3C3, 9P6 × 3P3
[A1] Accept unevaluated.
[B1] 3C3 × 6C2 or 15 seen anywhere, not multiplied or added
[M1] Seen as denominator of fraction
[A1] 5/42 OE, e.g. 15/126
[M1] 9! – k or 362880 – k, k an integer<362 880
[B1] 8! × 2(!) or 80 640 seen anywhere
[A1] Exact value
[M1] 7! × k, k positive integer > 1 If 7! not seen, condone 7 × 6 × 5 × 4 × 3 × 2 × (1) × k or 7 × 6! × k only
[M1] m × 2 × 7, m positive integer > 1
[A1]

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