Hi all, I posted this thread here and it was removed to electrical box (https://www.physicsforums.com/showthread.php?t=169778). In fact it is not an electrical. I hope this time it can be solved. There is a battery (B) and n bulbs (A1, A2... An). Now that I have to make a circuit from the battery to all the bulbs. There should be no loops. You can make it in series or trees, but no loops. The question is: ' how many ways to make a circuit are there? '. Here I draw a picture illustrating the case n=2. Because there are only 3 knots so there's no tree. Thanks.