O-LevelAdditional MathematicsPermutations and combinations4037/22 · Oct/Nov 2025 · Q55 Marks
A 6-character password is to be formed from the following characters. Letters b f g k m (5 characters) Numbers 3 5 7 9 (4 characters) Symbols * ! @ (3 characters) Each character can be used at most once in any 6-character password.
- (a)Find the number of 6-character passwords that can be formed if there are no further restrictions.[1]
- (b)Find the number of 6-character passwords that can be formed if the password starts and ends with a symbol.[2]
- (c)Find the number of 6-character passwords that can be formed if the password: • starts with either a symbol and then a number, or a number and then a symbol and • ends with 2 letters.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [B1] (a) 665 280
- [M1] (b) for 3 × 10 × 9 × 8 × 7 × 2 oe
- [A1] (b) 30 240
- [B1] (c) for a final answer of 13 440 or M1 for 2×3×4×8×7×5× 4 oe
- [A1] (c) 26 880
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