# . In how many of the distinct permutations of the letters in MISSISSIPPI do the four 1’s not come together?

SHAIK AASIF AHAMED
8 years ago
Hello student,
There are 11 letters in the word "MISSISSIPPI ", out of which: M=1, I=4, S=4, P=2.
Total # of permutations is$\frac{11!}{4!4!2!}$;
Number ofof permutations with 4 I's together is$\frac{8!}{4!2!}$. Consider 4 I's as one unit: {M}{S}{S}{S}{S}{P}{P}{IIII} - total 8 units, out of which {M}=1, {S}=4, {P}=2, {IIII}=1.
So # of permutations with 4 I'snot come togetheris:$\frac{11!}{4!4!2!}-\frac{8!}{4!2!}$.
Thanks and Regards
Shaik Aasif