O-LevelAdditional MathematicsPermutations and combinations4037/12 · Oct/Nov 2020 · Q88 Marks
Find the number of ways in which 12 people can be put into 3 groups containing 3, 4 and 5 people respectively.
- (a)Find the number of ways in which 12 people can be put into 3 groups containing 3, 4 and 5 people respectively.[3]
- (b)(i)4-digit numbers are to be formed using four of the digits 2, 3, 7, 8 and 9. Each digit may be used once only in any 4-digit number. Find how many 4-digit numbers can be formed if there are no restrictions,[1]
- (b)(ii)the number is even,[1]
- (b)(iii)the number is greater than 7000 and odd.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- B1 for one correct combination in a product of 2 or 3 combinations Must be numeric
- B1 for a second appropriate combination in the same product Must be numeric
- B1 for 27720
- B1 for 120
- B1 for 48
- B1 Starts with 7 or 9 -> 24
- B1 Starts with 8 -> 18
- B1 42
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