help!!!

I have a question,
:1.  On my way to work, I saw a thief _____ a wallet from a woman.
     A. steal     B. stealing    C. stole
2. On my way to work, I saw some boys _____ ball games on the playground.
     A. play     B. playing

Could someone tell me the answers of the two sentences?
and why choose that answer?????
for the second sentence, "playing" is the key,  but which is for the first????

Thank you.

i think both should take the verb+ing:

on my way to work, i saw a thief stealing (=who was stealing) a wallet from a woman.

on my way to work, i saw some boys playing (=who were playing) ball games on the playground.

on my way home, i saw a gangster who wanted to rob me.