A shipment of 40 television sets contains 3 defective units. How
many ways can a vending company can buy five of these units and
receive no defective units?
To solve this problem, we can use combination formula.
First, let's find the number of ways to choose 5 television sets out of the 40 available:
C(40, 5) = 40! / (5!(40-5)!) = 40! / (5!35!)
Now, let's find the number of ways to choose 5 television sets with no defective units:
C(37, 5) = 37! / (5!(37-5)!) = 37! / (5!32!)
The number of ways to choose 5 television sets with no defective units can be calculated by:
C(40, 5) - C(37, 5)
However, we need to consider that there are 3 defective units in the shipment, and we cannot choose any of them. So, we should subtract the number of ways to choose 5 television sets including at least one of the defective units.
There are 3 defective units, so we apply the same calculation with choosing 4 television sets instead of 5:
C(37, 4) = 37! / (4!(37-4)!) = 37! / (4!33!)
The number of ways to choose 4 television sets with no defective units can be calculated by:
C(40, 4) - C(37, 4)
Finally, we subtract the number of ways to choose 4 television sets including at least one of the defective units:
C(40, 4) - C(37, 4) - C(3, 1) = (40! / (4!(40-4)!) - (37! / (4!33!)) - 3
Simplifying the expression gives us the total number of ways to choose 5 television sets and receive no defective units.