Suppose that there are eight corporations competing for nine different contracts. If the contracts are awarded randomly, what is the probability that each corporation will get at least one contract?

For this distributing 9 contracts to 8 corporations, one corporation should get 2 contracts and others should get 1 contract to get atleast one contact. 8 ways to choose person getting 2 9c2 ways to allocate 2 to that person 7! ways to distribute the remaining 5, so favorable ways = 8*9c2*7! each contract has 8 choices for allocation, so total ways = 8^7 Pr = 8*9c2*7!/8^7 = 0.0430