Question

How many permutations are there of the 11 letters in MISSISSIPPI

1. taken all together?

2. all the I’s not come together?

Answer 1

1. In the word MISSISSIPPI there are 11 letters, of which S appears 4 times, I appears 4 times, P appears 2 times and the rest all are different.

Therefore the total number of ways is \(\frac{11 !}{4 ! \times 4 ! \times 2 !}\)= 34650.

2. 4 I’s are kept together and should be counted as one unit, then there are 8 units. The number of ways is \(\frac{8 !}{4 \times 2 !}\) = 840. 

Therefore the I’s not come together 

= Total arrangements – 4 I’s together.

= 34650 – 840 = 33810.