Q.10. In how many of the distinct permutations of the letters in MISSISSIPPI do the
four I’s not come together?
In the given word MISSISSIPPI, I appears 4 times, S appears 4 times, M appears 1 time and P appear 2 times.
Therefore, the number of distinct permutations of letters of the given word is
There are 4 I's in the given word. When they occur together they are treated as a single object for the time being. This single object with the remaining 7 objects will be 8 objects.
These 8 objects in which there are 4Ss and 2Ps can be arranged in ways.
The number of arrangement where all I's occur together = 840.
Hence, the distinct permutations of the letters in MISSISSIPPI in which the four I's do not come together