2021 VJC P2 Q5

2021 VJC P2 Q5

6 marks

Prelims

Find the number of ways in which all twelve letters of the word MISSPELLINGS can be arranged if

both the I’s are placed at the beginning and both the L’s are placed at the end,[1]
between any two S’s, there must be at least \(4\) other letters.[3]

A group of \(8\) letters is randomly selected from the letters of the word MISSPELLINGS. Find the probability that all \(8\) letters are distinct.[2]

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Answer:(i) \(6720\); (ii) \(362880\); P(all distinct) \(= \dfrac{4}{165}\)

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