A six-character password is to be made from the following eight characters. Digits: 1, 3, 5, 8, 9 Symbols: *, $, # No character may be used more than once in a password. Find the number of different passwords that can be chosen if

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [1] B1 20160
2. [1] B1 for 5P4 or 6×5×4×3(=360) for 'inner' characters or 5P2 or 4×5(=20) for 'outer' characters Must be part of a product
3. [1] B1 7200
4. [1] B1 for 3P3 or 3! or 6 for arrangements of symbols or 5P3 or 5×4×3 (= 60) for the digits Must be part of a product
5. [1] B1 360
6. [1] B1 May be implied by simplification e.g. n!/(n-5)!5! = 6 * (n-1)!/(n-5)!4! or n(n-1)(n-2)(n-3)(n-4)/5! = 6 * (n-1)(n-2)(n-3)(n-4)/4!
7. [1] M1 Simplification of either the numerical factorials or the algebraic factorials
8. [1] A1 n=30