1/26/15 Lecture
I was a little bit lost today with the example regarding finding the pattern with 3 people that can't stand next to each other out of 7 people. There's 4 non-special people so why is it 5 choose 3 to find the pattern? Can someone please explain this to me? Thanks in advance!
martha2A: Jan. 26, 2015, 9:09 p.m.
I'm going to attempt to explain with a diagram ^_ ^ _ ^ _ ^ _ ^ each line represents one of the 4 regular people. The 3 special people can stand anywhere in between these four people since they don't want to stand next to each other so the arrows are the 5 possibilities of where the three people can stand. Therefore, in order to come up with a pattern we choose 3 spots for the special people to stand in out of 5 possible spots (^) where they are in between a regular person. Let me know if you need more clarification.
weisbart: Feb. 1, 2015, 10:51 a.m.
Martha2A, this is an excellent explanation! I like it very much. The carrots that you drew are the fingers that I draw, and the dashes are the spaces between. The rings fit on the fingers, one on each at most. The carrots are the places where the people (who can't stand next to each other) can stand.