I'm learning how the blockchain works. I've read that when someone (say Alice) send twice a transaction to two different peoples (Bob and Charlie) such that Alice has only enough to pay Bob or Charlie, not both, then the first validated block containing of the two transactions will be accepted and the other will be rejected.
My question is : What happens if the two transactions Alice -> Bob AND Alice -> Charlie are sent to the same node and that node validates its block ? Is it possible ? If not, why ?