The Magadha Empire ruled from 684 B.C - 320 B.C in India.
The reference of the Magadha Empire is found in the two great epics Ramayana and Mahabharata.
There were three dynasties who ruled the Magadha empire from 544 BC to 322 BC.
The first one was Haryanka dynasty (544 BC to 412 BC) , the second was Shisunaga Dynasty (412 BC to 344 BC) and the other one was Nandadynasty (344 BC-322 BC).
Bimbisara came from the Haryanka dynasty, ruled for 52 years from 544 B.C. to 492 B.C
Bimbisara was imprisoned by his son Ajatshatru who ruled Magadha empire from 492- 460 B.C. He murdered his father Bimbisara.
Bindusara was the son of Chandragupta Maurya , the founder of Maurya dynasty and ruled from 298 BC to 272 BC
He is also referred to as Amitraghata (amitra-enemy, ghata-slayer) in Sanskrit Literature. Strabo has named him Amitrochates or Allitrochades which are a greek version of the name Amitraghata. He had two sons Sumana & Ashoka. Ashoka later succeeded him, after his death.
Ashoka was the son of Bindusara. He was governor of Taxila and Ujjain during his father’s reign. Ashoka sat on the throne around 268 B.C after successfully defeating his brothers. Hence option 3 is correct.