Answer to Question #220868 in Statistics and Probability for carmen

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: $N=N_1-N_2=31500.$