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**babbagandu** The eleven letters of the word MISSISSIPPI are scrambled and then arranged in some order.

(1) What is the probability that the four I's are consecutive letters in the resulting arrangement?

(2) What is the conditional probability that the four I's are consecutive (event A), given B , where B is the event that arrangement starts with M and ends with S?

(3) What is conditional probability of A, as de¯ned above, given C, where C is the event that the arrangements ends with four consecutive S's?

I have the answers and have been sitting here trying to figure out the reasoning behind it, but I have had no luck. Can anybody help me out?

The answers are as follows

1.)

8*[(7!)/(1!*4!*2!)]/[(11!)/1!*4!*4!*2!)] = 4/165

2.)

6*[C(5,2)]/[(9!)/(4!*3!*2!)] = 1/21

3.)

4*[C(3,2)]/[(7!)/(1!*2!*4!)] = 4/35