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

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

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1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 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
askIITians faculty

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