O-LevelAdditional MathematicsPermutations and combinations4037/21 · May/June 2010 · Q25 Marks
In a singing competition there are 8 contestants. Each contestant sings in the first round of this competition.
- (i)In how many different orders could the contestants sing?[1]
- (ii)After the first round 5 contestants are chosen. In how many different ways can these 5 contestants be chosen?[2]
- (iii)These 5 contestants sing again and then First, Second and Third prizes are awarded to three of them. In how many different ways can the prizes be awarded?[2]
Mark scheme
Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.
- [B1] (i) 40320
- [M1] (ii) 8×7×6×5×4 or 8! / (5!x3!)
- [A1] (ii) 56
- [M1] (iii) uses 5, 4 and 3 only
- [A1] (iii) 60
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