O-LevelAdditional MathematicsPermutations and combinations4037/22 · May/June 2025 · Q58 Marks
A 4-digit number is to be formed using the digits 0, 2, 4, 5, 6 and 8. The 4-digit number must not start with 0. Any digit may be used at most once in the 4-digit number.
- (a)(i)Find how many 4-digit numbers can be formed.[1]
- (a)(ii)Find how many even 4-digit numbers can be formed.[2]
- (a)(iii)Find how many 4-digit numbers that are divisible by 5 can be formed.[2]
- (b)Solve the equation (n+1)xn+1 C12 = 33 (n - 10) x n C10.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [B1] 300
- [M1] Calculation for (ends with 0) + (ends with 2,4,6,8) e.g., (5 × 4 × 3 × 1) + (4 × 4 × 3 × 4)
- [A1] 252
- [M1] Calculation for (ends with 0) + (ends with 5) e.g., (5 × 4 × 3 × 1) + (4 × 4 × 3 × 1)
- [A1] 108
- [B2] Correct simplified equation: (n+1)² =33×12×11 oe, nfww (B1 for an equation with simplified algebraic component (n+1)² oe or simplified numerical component 33×12×11oe, nfww)
- [B1] n=65 dep on B2; must be the only solution
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