Check my answer!
19. q: after the death of muhammad there was not a successor in line. describe the two groups under islam that resulted and who they believed to be the true caliph. explain in detail. (5 points)
the two groups were the shiite and sunnis. the shiite supported ali ibn abi talib who was the cousin of muhammad and had married his daughter, fatima. they believed that muhammad had wanted ali to become leader. the sunnis were supporters of abu who was one of muhammad’s closest companions and also already the leader of the islamic community.

It is quite true though Abu Bakr (R.A) was made the Caliph by doing Qayas. 
Your answer is right but you want to go into details then you may ask :)

The Companions decided that Abu Bakr (R.A) was to become the Caliph through Qayas; the secondary source of Islamic Law (Shariah). The meaning of the word Qayas is comparison. The Companions saw that when once the Prophet was sick He asked Abu Bakr (R.A) to lead the prayers but as he was late Umar (R.A) started. When the Prophet heard Umar's voice and not Abu Bakr's he said to re read the prayers by that time Abu Bakr had arrived so then Abu Bakr lead the prayers.
Secondly they saw that Abu Bakr was the Prophets closest Companion and the childhood friend so they chose him.
The Shiyas were bitter because they believed that Ali (R.A) deserved Caliphate though it was not the desire of Ali (R.A) himself. 
The Sunni Shiyas problems got a lot worse during the times of Usman (R.A) who was the third Caliph.

Your answer will be a.