Question

a cartoon of batteries contains 2 defective batteries. in how many ways can the inspector choose three of the batteries and get

- none of the defective batteries

-one of the defective battereies

-both

Answer 1

Lets say there are N batteries in the cartoon.

Total Defective batteries = 2 ; No of non defective batteries = N-2

No of batteries chosen for inspection = 3

A. None of the batteries are defective : In this case , 3 batteries are to chosen from N-2 non defective batteries & this can be done in ways.

B. One of the battery is defective : In this case, out of 3 batteries selected, two non defectives are chosen from N-2 non defectives and one defective is chosen from the 2 defective batteries.

and this can be done in ways.

C. Both the batteries are defective : In this case, out of 3 batteries selected, one non defective is selected from N-2 & rest tow defectives are selected from the 2 defective batteries.

and this can be done in ways.

Hope I answered our question.