A shipment of 30 computers contains four that are defective. How many ways can a small business buy five of these computers and receive no defective ones
To find the number of ways to buy five computers without receiving any defective ones, we can use the concept of combinations.
1. First, let's determine the number of ways to choose five computers out of the 30 available computers. This can be calculated using the formula for combinations: nCr = n! / (r!(n-r)!), where n is the total number of items, and r is the number of items being chosen.
In this case, n = 30 (total number of computers) and r = 5 (number of computers being chosen).
Combination formula: C(30, 5) = 30! / (5!(30-5)!) = 30! / (5! * 25!)
2. However, we need to consider that four of these computers are defective and should not be chosen. So, we need to subtract the combinations where we choose the defective computers.
To find the number of ways to choose five computers from the four defective ones, we use the combination formula: C(4, 5) = 4! / (5!(4-5)!) = 4! / (5! * (-1)!) = 0
Since there are no possible ways to choose five computers from four defective ones, the result of C(4, 5) is 0.
3. Now, we subtract the number of combinations with defective computers from the total combinations to find the number of ways to buy five computers without receiving any defective ones.
Number of ways to buy five non-defective computers: C(30, 5) - C(4, 5) = 30! / (5! * 25!) - 0 = 142506
Therefore, there are 142,506 ways for the small business to buy five computers and receive no defective ones from the shipment of 30 computers.