SOLUTION: A company is considering bids submitted by seven different firms for three different contracts. In how many ways can the contracts be awarded among the firms if no firm is to re

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Question 631247: A company is considering bids submitted by seven
different firms for three different contracts. In how many ways
can the contracts be awarded among the firms if no firm is to
receive more than two contracts?

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
There are 7 ways to award each contract.
That gives you a total of 7%5E3 ways of awarding them.
Included in those 7%5E3 ways there are 7 ways to award all 3 contracts to the same firm.
Since we do not want to give all 3 contracts to the same firm, we subtract those 7 choices from the total to find
7%5E3-7=7%287%5E2-1%29=7%2A48=336 ways to award the contract so that no firm
receives more than two contracts.