A-LevelMathematicsProbability and statistics9709/53 · Oct/Nov 2020 · Q36 Marks
A committee of 6 people is to be chosen from 9 women and 5 men. The 9 women and 5 men include a sister and brother.
- (a)Find the number of ways in which the 6 people can be chosen if there must be more women than men on the committee.[3]
- (b)Find the number of ways in which the committee can be chosen if the sister and brother cannot both be on the committee.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [M1] Correct number of ways for either 5 or 4 women, accept unsimplified
- [M1] Summing the number of ways for 2 or 3 correct scenarios (can be unsimplified), no incorrect scenarios.
- [A1] 1974
- [M1] 14C6 - a value
- [M1] 12Cx or 12C4 seen on its own or subtracted from their total, x ≤ 6, n < 13
- [A1] 2508
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →