A-LevelMathematicsProbability and statistics9709/52 · Feb/Mar 2024 · Q610 Marks

A new village social club has 10 members of whom 6 are men and 4 are women. The club committee will consist of 5 members.

(a)In how many ways can the committee of 5 members be chosen if it must include at least 2 men and at least 1 woman?[4]
(b)The 10 members of the club stand in a line for a photograph. How many different arrangements are there of the 10 members if all the men stand together and all the women stand together?[2]
(c)For a second photograph, the members stand in two rows, with 6 on the back row and 4 on the front row. Olly and his sister Petra are two of the members of the club. How many different arrangements are there of the 10 members in which Olly and Petra stand next to each other on the front row?[4]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2024). The mark or mark type is shown in brackets.

[M1] 6Ca x 4Cb with a + b = 5 seen, no extra terms.
[B1] Correct outcome/value for one clearly identified scenario. Accept unsimplified, www. Condone use of × 5C0.
[M1] Add values of three correct scenarios, no incorrect scenarios, no repeated scenarios. Condone 'Ca × 4Cb with a + b = 5 to identify M, W for this mark.
[A1] Not dependent on B1. If A0 scored, SC B1 for 240 www.
[M1] 6! × 4! × k; k = 1, 2. 1 can be implied.
[A1] Cao. If M0 scored, SC B1 for 34 560 www.
[M1] 8! × g, g an integer greater than 1.
[M1] h! × 3 × j; h = 7, 8, 9; j = 1, 2 (1 may be implied). Condone 3C1 for 3.
[M1] h!× 3 × 2; h = 7, 8, 9. Condone 2C1 for 2. (Condone h! × 3! For M1M1).
[A1] If A0 Scored, SC B1 for 241 920.

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