Final answer:
The number of ways a restaurant can buy 3 microwave ovens without receiving a defective unit is 56, and the number of ways they can buy 3 ovens and receive exactly one defective unit is also 56.
Step-by-step explanation:
The question involves combinatorial mathematics, specifically the calculation of combinations. There are 10 microwave ovens, with 2 being defective and 8 non-defective. The task is to find the number of ways a restaurant can purchase 3 units in different scenarios.
Scenario a) No defective units:
To calculate the number of combinations without any defective units, the restaurant would choose 3 out of the 8 non-defective units. The combination formula is C(n, k) = n! / (k! * (n - k)!), where 'n' represents the total number of items to choose from, and 'k' is the number of items to choose.
C(8, 3) = 8! / (3! * (8 - 3)!) = 56
Scenario b) One defective unit:
For one defective unit, the restaurant has 2 defective and 8 non-defective units to choose from. They would select 1 defective and 2 non-defective units, which involves calculating two separate combinations and multiplying them together.
C(2, 1) * C(8, 2) = 2 * 28 = 56