A-LevelMathematicsProbability and statistics9709/51 · May/June 2023 · Q25 Marks
A different committee of 6 people is to be chosen from 6 men and 8 women. Three of the 6 men are brothers.
- (a)Find the number of ways in which a committee of 6 people can be chosen from 6 men and 8 women if it must include 3 men and 3 women.[2]
- (b)Find the number of ways in which this committee can be chosen if there are no restrictions on the numbers of men and women, but it must include no more than two of the brothers.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [M1] ⁶C₃ × b or c × ⁸C₃ seen. b, c integers ≥ 1 (1 may be implied).
- [A1]
- [B1] ³Cₓ × ¹¹C₆₋ₓ, with x = 1 or 2 seen.
- [M1] Add values of 3 correct scenarios, (may be identified by the appropriate calculations) no incorrect/repeated scenarios, condone use of permutations.
- [A1] Only dependent on the M mark. SC B1 for the correct calculation or 2838 seen WWW.
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