Question

a

Answer 1

There is one way in which none of the bulbs are defective.
There are 5 ways in which one of the bulbs is defective.
There are 5C2 ways in which 2 of the bulbs are defective.

Answer 2

There is only one way in which all of the bulbs are defective.
If the 5 bulbs were numbered 1 ~5, then if exactly one bulb is defective it can be either number 1, number 2, number 3, number 4 or number 5. Therefore there are 5 ways in which one of the bulbs is defective.
If 2 bulbs are defective this can happen in the 5C2 combinations of the 5 bulbs taken 2 at a times. 5C2 = 10.
Therefore the number of different ways there can be at most 2 non-working light bulbs is
1 + 5 + 10 = 16 ways.

Answer 3

*....taken 2 at a time.