O-LevelAdditional MathematicsPermutations and combinations4037/22 · Oct/Nov 2024 · Q78 Marks
A class of 10 students includes Abby and Ben.
- (a)(i)A group of 5 students is to be selected from the class. Find the number of possible groups in the following cases. There are no restrictions.[1]
- (a)(ii)A group of 5 students is to be selected from the class. Find the number of possible groups in the following cases. The group includes both Abby and Ben.[2]
- (a)(iii)A group of 5 students is to be selected from the class. Find the number of possible groups in the following cases. The group includes either Abby or Ben, but not both.[2]
- (b)All 10 students are arranged in a line. How many arrangements are possible if there are exactly three students between Abby and Ben?[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.
- [B1] 252
- [B2] 56 [B1] for ⁸C₃ or 8!/(5!3!) oe
- [B2] 140 [B1] for ⁹C₄ × 2 oe or ¹⁰C₅ – ⁸C₅ – ⁸C₃ oe
- [B3] 483 840 [B2] for 8! × 6 [× 2] or 241 920 oe
- [B1] for 8! or 40320 or 8! × 2 or 80640
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