O-LevelAdditional MathematicsPermutations and combinations4037/22 · May/June 2012 · Q1010 Marks
A team of 7 people is to be chosen from 5 women and 7 men. Calculate the number of different ways in which this can be done if
- (a)(i)there are no restrictions,[1]
- (a)(ii)the team is to contain more women than men.[3]
- (b)(i)How many different 4-digit numbers, less than 5000, can be formed using 4 digits 1, 2, 3, 4, 5 and 6 if no digit can be used more than once?[4]
- (b)(ii)How many of these 4-digit numbers are divisible by 5?[2]
Mark scheme
Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.
- [B1] (a)(i) ⁷C₅+₇C₂ (Total (5+7)C7 = 12C7)
- [M1] (a)(ii) 4W, 3M and 5W, 2M
- [B1] (a)(ii) ⁵C₄ × ⁷C₃ or ⁵C₅ × ⁷C₂
- [A1] (a)(ii) 196
- [M1] (b)(i) 4×5×4×3 or ⁴P₃ × ⁶P₃
- [A1] (b)(i) 240
- [M1] (b)(ii) 4×4×3×1 or ⅙ × (240)
- [A1] (b)(ii) 48
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