The bulbs will provide more illumination when connected in parallel as each bulb will get the required voltage/current and their illuminations will be added, In case the bulbs are connected in series, they will not get the required voltage and may not glow.
The bulbs should be connected in parallel because each bulb will show its maximum power or total resistance decrease hence greater current may be, drawn from the cell.
Advantages of parallel arrangement :
(i) The voltage across each device is same and it can take current as per its resistance.
(ii) If one device is damaged, then others continue to work properly.
