O-LevelAdditional MathematicsPermutations and combinations4037/12 · Oct/Nov 2023 · Q78 Marks
A 6-digit number is to be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Each digit can be used only once in any 6-digit number. A 6-digit number cannot start with 0. (i) Find how many 6-digit numbers can be formed. (ii) Find how many of these 6-digit numbers are divisible by 5.
- (a)A 6-digit number is to be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Each digit can be used only once in any 6-digit number. A 6-digit number cannot start with 0. (i) Find how many 6-digit numbers can be formed. (ii) Find how many of these 6-digit numbers are divisible by 5.[4]
- (b)A committee of 7 people is to be chosen from 6 doctors, 10 nurses and 8 dentists. (i) Find the number of committees that can be chosen. (ii) Find the number of committees that can be chosen if all the doctors have to be on the committee. (iii) Find the number of committees that can be chosen if there has to be at least one dentist on the committee.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [1] (a)(i) B1
- [3] (a)(ii) B1
- [3] (a)(ii) B1
- [3] (a)(ii) B1
- [1] (b)(i) B1
- [1] (b)(ii) B1 Do not isw subsequent work
- [2] (b)(iii) M1 Allow attempts at 7 options, but must have all of them:
- [2] (b)(iii) A1 May come from 24C7 – 16C7
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