These are the ones we use (though the other 2 are grammatically fine):
We need exercise.
He is a man of amibition.
I'm afraid I must guess that it is a matter of usage, collocation and set phrase. For instance, 'a man of + ambition/honor/strength/means' is a semi-fixed phrase.
I'm afraid I must guess that it is a matter of usage, collocation and set phrase. For instance, 'a man of + ambition/honor/strength/means' is a semi-fixed phrase.