**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!

= 11*10*9*8*7*6*5*4!/4!*4*3*2*1*2*1

=11*10*9*8*7*6*5/4*3*2*1*2*1

= 34650

There are 4 Is in the given word. When they occur together, they are treated as a single object **IIII** 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 **8!/4!2! ways** i.e., **840 ways.**

Number of arrangement 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**