A shipment of 10 microwave ovens contains two defective units. in how many ways can a restaurant buy three of these units and receive

a. no defective units

b. one defective unit

Number of microwaves = 10

Defective microwaves = 2

Non-defective microwaves = 10 - 2 = 8

Number of microwaves bought = 3

Part (a) : No defective units

This means 3 will only be bought from the 8 non-defective microwaves.

Number of ways of buying 3 from 8 = 8C3 = 8!/{3! * (8-3) !} = 56 ways.

Part (b) : One defective unit

This means that 2 units will be selected from 8 non-defective while 1 unit will be selected from 2 defective units.

Therefore,

Number of ways of selecting 2 from and 1 from 2 = (8C2) * (2C1) = 28*2 = 56 ways.