Question

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?

Answer 1

To find the probability that each corporation will get at least one contract out of eight corporations competing for nine different contracts, we can use the concept of permutations and the principle of inclusion-exclusion.

Step-by-step explanation:

To find the probability that each corporation will get at least one contract, we can use the concept of permutations. Since there are 8 corporations and 9 contracts, we can calculate the total number of ways to assign the contracts to the corporations without any restrictions, which is 9! (9 factorial).

Next, we need to find the number of ways that each corporation gets at least one contract. This can be calculated using the principle of inclusion-exclusion. We subtract the number of ways that at least one corporation doesn't get a contract from the total number of permutations.

The number of ways that at least one corporation doesn't get a contract can be calculated by assigning 9 contracts to 7 corporations, which is 7! (7 factorial).

Finally, we can calculate the probability by dividing the number of ways that each corporation gets at least one contract by the total number of permutations:

Probability = (9! - 7!) / 9!

Answer 2

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