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In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
Asked by Aksabanu Last Modified
Answer 
Harshit Bhardwaj
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
There are 4 Is in the given word. When they occur together, they are treated as a single object 
for the time being. This single object together with the remaining 7 objects will account for 8 objects.
These 8 objects in which there are 4 Ss and 2 Ps can be arranged in
ways i.e., 840 ways.
Number of arrangements where all Is occur together = 840
Thus, number of distinct permutations of the letters in MISSISSIPPI in which four Is do not come together = 34650 – 840 = 33810
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