A-LevelMathematicsProbability and statistics9709/51 · May/June 2022 · Q26 Marks
There are 6 men and 8 women in a Book Club. The committee of the club consists of five of its members. Mr Lan and Mrs Lan are members of the club.
- (a)In how many different ways can the committee be selected if exactly one of Mr Lan and Mrs Lan must be on the committee?[2]
- (b)In how many different ways can the committee be selected if Mrs Lan must be on the committee and there must be more women than men on the committee?[4]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [M1] 12C4 × h g = 12, 13, h = 1,2
- [A1] 990
- [M1] rC_x x 6C_4-r, for r = 2, 3 or 4
- [B1] Outcome for one identifiable scenario correct, accept unevaluated
- [M1] Add outcomes for 3 identifiable correct scenarios Note: if scenarios not labelled, they may be identified by seeing 7C_r x 6C_s r + s = 4 to imply r women and s men for both B & M marks only
- [A1] 560
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