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Question
Find the distinct permutations of the letters of the word MISSISSIPPI?
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Solution
The given word is MISSISSIPPI.
Number of letters in the word = 11
Number of S’s = 4
Number of I’s = 4
Number of P’s = 2
Number of M’s = I
Hence the total number of distinct words
= `(11!)/(4! xx 4! xx 2! xx 1!)`
= `(11 xx 10 xx 9 xx 8 xx 7 xx 6 xx 5 xx 4!)/(4 xx 3 xx 2 xx 1 xx 4! xx 2 xx 1 xx 1)`
= `(11 xx 10 xx 9 xx 8 xx 7 xx 6 xx 5)/(4 xx 3 xx 2 xx 2)`
= `(11 xx 10 xx 9 xx 8 xx 7 xx 6 xx 5)/(8 xx 6)`
= 10 × 10 × 9 × 7 × 5
= 34,650
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