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
There are 40-3=37 non-defective units.
Number of ways
= 37 choose 5
= (37,5)
= 37!/(5!(37-5)!)
Bottled Water Consumption (Problem 31, page 383)
Department of Agriculture claims that the mean consumption of coffee by the person in the United States is ... A random sample of 120 people in the United States shows that the mean coffee consumption is 23.5 gallons per year with a standard .
To find the number of ways the vending company can buy five television sets without receiving any defective units, we can apply the concept of combinations.
First, we need to determine the number of "good" television sets in the shipment. Since the shipment contains 40 television sets, and 3 of them are defective, this means there are 40 - 3 = 37 good television sets.
The number of ways the vending company can choose 5 television sets from these 37 good sets can be calculated using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
Here, n represents the total number of items to choose from (37 in this case), and r represents the number of items we want to choose (5). The exclamation mark denotes the factorial operation.
Let's calculate it:
C(37, 5) = 37! / (5! * (37 - 5)!)
37! = 37*36*35*34*33*32*31*30*29*28*27*26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
5! = 5*4*3*2*1
32! = 32*31*30*29*28*27*26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
C(37, 5) = (37*36*35*34*33)/(5*4*3*2*1)
Calculating this expression, we find:
C(37, 5) = 153,393
Therefore, the vending company can buy five television sets from this shipment in 153,393 different ways without receiving any defective units.