In how many ways can 3 different contracts be distributed among 5 different firms, if one firm can be awarded multiple contracts?

Question

In how many ways can 3 different contracts be distributed among 5 different firms, if one firm can be awarded multiple contracts?

Answer 1

the first contract can go to firm1, firm 2, firm 3, firm 4, or firm 5

the second can go to 1,2,3,4, or 5 also (one firm can be awarded multiple contracts)

the third can go to 1,2,3,4, or 5 also (same reasoning here)

5*5*5=125 ways

sometimes it helps to make a similar more simple problem and you can get the idea from that...

how many ways can 2 contracts be distributed among 3 firms ?

contracts are A and B, firms are 1, 2, and 3

firm 1     firm 2     firm 3

A            B

A                         B

              A           B

B            A

B                         A

              B           A

AB         

              AB

                           AB

9 ways

contract A can go to 1,2, or 3

contract B can go to 1,2, or 3

3*3=9 ways