O-LevelAdditional MathematicsPermutations and combinations4037/22 · Oct/Nov 2019 · Q36 Marks
A 5-digit code is formed using the following characters. Letters a c e i o u Numbers 1 2 3 4 5 6 Symbols @ * # No character can be repeated in a code. Find the number of possible codes if
- (i)there are no restrictions,[2]
- (ii)the code starts with a symbol followed by two letters and then two numbers,[2]
- (iii)the first two characters are numbers, and no other numbers appear in the code.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- M1 14P5 or 14 × 13 × 12 × 11 × 10
- A1 240 240 cao
- M1 3P1 x 5P2 x 6P2 or 3 × (5 × 4) × (6 × 5) Two of the three elements multiplied by ...
- A1 = 1800
- M1 6P2 x 8P3 or (6 × 5) × (8 × 7 × 6) One element multiplied by ... Clear intention to multiply
- A1 = 10080
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