How did Romes defeats help lead to their later victory over the Samnites?

The first of these wars was the result of Rome's intervention to rescue the Campanian city of Capua from a Samnite attack. The second one was the result of Rome's intervention in the politics of the city of Naples and developed into a contest over the control of much of central and southern Italy. The third war also involved a struggle over the control of this part of Italy. The wars extended over half a century and the peoples to the east, north, and west of Samnium (land of the Samnites) as well as the peoples of central Italy north of Rome (the Etruscans, Umbrians, and Picenti) and the Senone Gauls got involved to various degrees and at various points in time. The Samnites were one of early Rome's most formidable rivals.

The results were Roman control over much of central Italy and part of southern Italy (the modern regions of Lazio, Abruzzo, Molise, Campania and Basilicata and Northern Apulia)

the answer would be choice c, cave paintings.