A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2019 · Q69 Marks
The word STEEPLECHASE has 12 letters.
- (i)Find the number of different ways in which all 12 letters of the word STEEPLECHASE can be arranged so that all four Es are together.[1]
- (ii)Find the number of different ways in which all 12 letters of the word STEEPLECHASE can be arranged so that the Ss are not next to each other.[4]
- (iii)Four letters are selected from the 12 letters of the word STEEPLECHASE. Find the number of different selections if the four letters include exactly one S.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [B1] Exact value
- [B1] Total no of ways = 12!/(2!4!) = 9979200 (A)
- [B1] With Ss together = 11!/4! = 1663200 (B)
- [M1] Correct or (12!/m) - (8!/n), m,n integers > 1 or their identified total – their identified Ss together
- [A1] Exact value
- [M1] Cx seen alone or times K>1
- [B1] C3 or C2 or 'C1 alone
- [M1] No extras
- [A1]
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