O-LevelAdditional MathematicsPermutations and combinations4037/12 · May/June 2022 · Q87 Marks
A team of 6 people is to be chosen from 10 people. Two of the people are sisters who must not be separated. Find the number of different teams that can be formed.
- (a)A team of 6 people is to be chosen from 10 people. Two of the people are sisters who must not be separated. Find the number of different teams that can be formed.[3]
- (b)(i)A 6-character password is to be chosen from the following characters. Digits 2 4 8 Letters X y Z Symbols * # ! No character may be used more than once in any password. Find the number of different passwords that may be chosen if there are no other restrictions,[1]
- (b)(ii)the password starts with two letters and ends with two digits.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [B1] With the sisters: 70 or ⁸C₄ oe
- [B1] Without the sisters: 28 or ⁸C₆ oe
- [B1] Total: 98
- [B1] 60480
- [1] B1 6 or ³P₂ oe seen twice
- [1] B1 20 or ⁵P₂ oe seen
- [1] B1 Total number of ways: 720
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 →