Question

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

Answer 1

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.