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Question
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together ?
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together ?
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Solution
In the given word MISSISSIPPI, I appears 4 times , S appears 4 times, P appears 2 times, and M appears just once.
Therefore, number of distinct permutations of the letters in the given word =11!4×4×2=34650
There are 4I's in the given word. When they occur together, they will be treated as a single object for the time being. This single object together with the remaining 7 objects will account for 8 objects.
In these 8 objects, there are 4 Ss and 2 Ps which can be arranged in =8!4×2=840
Thus, number of distinct permutations of the letters of MISSISSIPPI in which 4 I's do not come together = 34650 - 840 = 33810
Therefore, number of distinct permutations of the letters in the given word =11!4×4×2=34650
There are 4I's in the given word. When they occur together, they will be treated as a single object for the time being. This single object together with the remaining 7 objects will account for 8 objects.
In these 8 objects, there are 4 Ss and 2 Ps which can be arranged in =8!4×2=840
Thus, number of distinct permutations of the letters of MISSISSIPPI in which 4 I's do not come together = 34650 - 840 = 33810
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