O-LevelAdditional MathematicsPermutations and combinations4037/11 · May/June 2021 · Q69 Marks
(a) (i) Find how many different 5-digit numbers can be formed using the digits 1, 3, 5, 6, 8 and 9. No digit may be used more than once in any 5-digit number. (ii) How many of these 5-digit numbers are odd? (iii) How many of these 5-digit numbers are odd and greater than 60000? (b) Given that 45×"C4 = (n + 1)x"+1C5, find the value of n.
- (a)(i)Find how many different 5-digit numbers can be formed using the digits 1, 3, 5, 6, 8 and 9. No digit may be used more than once in any 5-digit number.[1]
- (a)(ii)How many of these 5-digit numbers are odd?[1]
- (a)(iii)How many of these 5-digit numbers are odd and greater than 60000?[3]
- (b)Given that 45×ⁿC₄ = (n + 1)×ⁿ⁺¹C₅, find the value of n.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [1] B1
- [1] B1
- [3] B1 [Starts with 6 or 8]: 192
- [3] B1 [Starts with 9]: 72
- [3] B1 Total = 264
- [3] (B1) Alternative [Ends with 9]:48
- [3] (B1) [Ends with 1,3 or 5]:216
- [3] (B1) Total = 264
- [4] B1
- [4] M2 M1 for 15 OR M1 for n + 1 M1 for n² + 2n-224=0 oe M1 for (n-14)(n+16)=0
- [4] A1
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