Consider these problems: 1. In how many ways can 7 boys be seated around a round table? 2. If seven beads of different colors are put on a ring how many different desighns can be made? 3. I have six books with identical black bindings, 8 with identical red bindings. In how many ways can I arrange them on a shelf so as to give the same apperance? 4. In how many ways can we choose a team of 5 from 10 boys? Recently I've started to study probablity, the books I'm reading have a chapter on permutation and combination before the one on probablity. Now the problem is that I think there are so many pitfalls in per & com problems. For example in the first problem my answer was 7! but the book said that it's 7!/7. In the second one I got 7!/7 (from what I learnt from the first one) and the right answer is 7!/7*2. In the third one I even didn't get the quetion and in the forth one my answer was (10C5) but the correct one was (10C5)/2 :yuck: I can figure it out in two ways: 1. That's all a matter of experience and after solving some problems, I will do better. 2. In the next years of my study there are some mathematics that after learning them all the problems of per&comb will seem easy to me. Which one is the case? And the important question for me is: Is understanding all of them necessary for learning probablity or I can loosen it up for now and get right into studying probablity?