if you have two 5 watt bulbs connected in series and then in parellel:

a) Which circuit arrangement will give you brighter bulbs? Explain your answer....

b) Which of these arrangements will allow the other bulb to continue glowing if one of the bulbs is removed?

In parallel, the two bulbs burn independently of the other. So b is parallel. For a, look at the resistance of the two bulbs in series versus the resistance of the bulbs in parallel.