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Question
If the letters of the word 'MISSISSIPPI' are written down at random in a row, what is the probability that four S's come together.
Solution
There are 11 letters in the word ‘MISSISSIPPI’ which can be arranged in 11! ways.
Number of the letter S = 4
Let us consider the four S's in the given word as one letter.
So, when the four letters are clubbed together, we have (SSSS) MIIIPPI. We can arrange eight letters in a row in 8! ways.
Also, the four S's can be arranges in 4! ways.
Hence, required probability = \[\frac{8! \times 4!}{11!} = \frac{8! \times 4 \times 3 \times 2}{11 \times 10 \times 9 \times 8!} = \frac{4 \times 3 \times 2}{11 \times 10 \times 9} = \frac{4}{165}\]
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