Eleven books consisting of 5 financial management, 4 marketing management and 2 system management are placed on a shelf at random order. What is the probability that the books of each kind are all together.
(Probability of an event) = (Favorable) / (Total)
The total number of ways to arrange 11 books in a row is 11!.
3 groups of books: financial management (F), marketing management (M) and system management (S), can be arranged in 3! ways: FMS, FSM, MFS, MSF, SFM, and SMF (this way all the books of each kind will be together). Now, books in F itself can be arranged in 5! ways, in M in 4! ways and in S in 2! ways. Hence, the total number of ways to arrange books so that books of each kind are together is 3!*5!*4!*2!.
P = (3!*5!*4!*2!) / 11! = 1/1155.
Hope it's clear.
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