O-LevelAdditional MathematicsPermutations and combinations4037/12 · May/June 2020 · Q410 Marks
Find how many different 5-digit numbers can be formed using the digits 1, 2, 3, 5, 7 and 8, if each digit may be used only once in any number.
- (a)(i)Find how many different 5-digit numbers can be formed using the digits 1, 2, 3, 5, 7 and 8, if each digit may be used only once in any number.[1]
- (a)(ii)How many of the numbers found in part (i) are not divisible by 5?[1]
- (a)(iii)How many of the numbers found in part (i) are even and greater than 30000?[4]
- (b)The number of combinations of n items taken 3 at a time is 6 times the number of combinations of n items taken 2 at a time. Find the value of the constant n.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [1] 720
- [1] 600
- [1] Starting with 8: 1×4×3×2×1 = 24
- [1] May be considering each case separately, need all three cases for M1
- [1] Starting with 3, 5 or 7: 3×4×3×2×2=144
- [1] Total = 168
- [1] nC3 = 6nC2
- [1] n(n-1)(n-2)/3! = 6n(n-1)/2!
- [1] Valid attempt to solve, must have at least one previous B mark
- [1] n = 20
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