A shipment of 35 computers contains three that are defective. How many ways can a small business buy four of these computers and receive no defective ones.
a. 128
b. 35960
c. 52360
d. 6545
b. 35960
To find the number of ways a small business can buy four computers from a shipment of 35 without receiving any defective ones, we can use a combination formula.
First, let's find the number of ways to choose four computers from the 35 available. This can be calculated using the combination formula:
C(n, r) = n! / (r!(n - r)!)
Where n is the total number of computers and r is the number of computers to be selected.
In this case, n = 35 (total number of computers) and r = 4 (number of computers to be selected).
C(35, 4) = 35! / (4!(35 - 4)!)
= (35 * 34 * 33 * 32) / (4 * 3 * 2 * 1)
= 52,360
So there are 52,360 ways to choose four computers from the shipment of 35.
Now, let's consider the restriction that none of the selected computers should be defective. Since there are three defective computers in the shipment, we need to find the number of ways to choose four computers from the remaining 32 non-defective computers.
Using the same combination formula:
C(32, 4) = 32! / (4!(32 - 4)!)
= (32 * 31 * 30 * 29) / (4 * 3 * 2 * 1)
= 35,960
Therefore, there are 35,960 ways to select four computers from the shipment of 35 without any defective ones.
Hence, the answer is option b. 35960.