Five firms FIF2FS each offer bids on three separate contract

Five firms, FI,F2,--,FS each offer bids on three separate contracts C1 C2 andC3 Any one firm will be awarded at most one contract. The contracts are quite different, so an assignment of C1 to F1, is to be distinguished from an assignment of C2 to F1. How many sample points are there in the experiment involving assignment of contracts to the firms? (No need to list them all.) Under the assumption of equally likely sample points, find the probability that F3 is never awarded a contract.

Solution

(a) C1 has F1 to F5 5 choice, so do C2 and C3 so total 5^3 =125 (b) C1 assigned to F1, F2, F4 and F5 4 choice, so do C2 and C3. 4^3=64 This is the case that F3 has no contract. Then F3 has at least one contract is 125-64=61 Probability is 61/125=.488