A-LevelMathematicsProbability and statistics9709/53 · May/June 2020 · Q710 Marks

Find the number of different possible arrangements of the 9 letters in the word CELESTIAL.

(a)Find the number of different possible arrangements of the 9 letters in the word CELESTIAL.[1]
(b)Find the number of different arrangements of the 9 letters in the word CELESTIAL in which the first letter is C, the fifth letter is T and the last letter is E.[2]
(c)Find the probability that a randomly chosen arrangement of the 9 letters in the word CELESTIAL does not have the two Es together.[4]
(d)5 letters are selected at random from the 9 letters in the word CELESTIAL. Find the number of different selections if the 5 letters include at least one E and at most one L.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

[B1] 9! / (2!2!) = 90 720
[M1] 6! / 2!
[A1] 360
[M1] 2 Es together = 8! / 2! (=20160)
[M1] Es not together=90720-20160=70560
[M1] Probability = 70560 / 90720
[A1] 7/9 or 0.778
[M1] Scenarios are: E L _ _ _ 5C3 10; E E L _ _ 5C2 10; E E _ _ _ 5C4 5; E E _ _ _ 5C3 10
[M1] Summing the number of ways for 3 or 4 correct scenarios
[A1] Total = 35

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