Question

How many permutations can be made from all the letters in the word "MISSISSIPPI", under the condition that "M" is not in the middle?

Answer 1

Number of permutation in the word "MISSISSIPPI": $N_1=\frac{11!}{4!4!2!}=34650.$

Number of permutations if "M" is in the middle: $N_2=\frac{10!}{4!4!2!}=3150.$

Number of permutations if "M" is not in the middle: $N=N_1-N_2=31500.$