O-LevelAdditional MathematicsPermutations and combinations4037/21 · May/June 2018 · Q35 Marks
A 7-character password is to be selected from the 12 characters shown in the table. Each character may be used only once. Characters Upper-case letters | A | B | C | D Lower-case letters | e | f | g | h Digits | 1 | 2 | 3 | 4 Find the number of different passwords
- (i)if there are no restrictions,[1]
- (ii)that start with a digit,[1]
- (iii)that contain 4 upper-case letters and 3 lower-case letters such that all the upper-case letters are together and all the lower-case letters are together.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [1] (i) (12P7 =) 3991680
- [1] (ii) (4 × 11P6 = ) 1330560
- [2] (iii) 4! x 4! x 2 oe
- [1] (iii) M1 for 4! × 4! oe only or 4P4 x 3P3 oe only
- [1] (iii) 1152
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