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The letters of MISSISSIPPI are arranged so that the four S's are all separated from one another. How many such arrangements exist?

Competition practicePermutations & Combinations

A34650
B7350
C105
D4410

Step-by-Step Solution

Arrange the 7 non-S letters (M,

I \times 4, P \times 2) : \frac{7 !}{4 ! 2 !} = 105

. They leave 8 gaps; place the 4 S's in 4 different gaps:

^{8} C_{4} = 70.105 \times 70 = 7350

.

Answer: B) 7350

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