A-LevelMathematicsProbability and statistics9709/52 · May/June 2020 · Q69 Marks
Find the number of different ways in which the 10 letters of the word SUMMERTIME can be arranged...
- (a)Find the number of different ways in which the 10 letters of the word SUMMERTIME can be arranged so that there is an E at the beginning and an E at the end.[2]
- (b)Find the number of different ways in which the 10 letters of the word SUMMERTIME can be arranged so that the Es are not together.[4]
- (c)Four letters are selected from the 10 letters of the word SUMMERTIME. Find the number of different selections if the four letters include at least one M and exactly one E.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [M1] 8!/3!
- [A1] 6720
- [B1] Total number = 10!/(2!3!) (302400) (A)
- [B1] With Es together = 9!/3! (60480) (B)
- [M1] Es not together = their (A) – their (B)
- [A1] 241920
- [M1] Scenarios: EMMM ⁵C₀=1 EMM ⁵C₁=5 EM ⁵C₂=10
- [M1] Summing the number of ways for 2 or 3 correct scenarios
- [A1] Total = 16
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