# Permutation and Combination

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?

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Combinatorics,,, which is the math involved with counting... which is what you're studying right now, is very important in applications of many different fields.

Just so you know the probability of an outcome is equal the number of ways the desired outcome could happen divided by the number of all possible outcomes.
Therefore you must be able to count both of those outcomes, which is what your learning right now.... so it is essential that you learn them in order to move on to probability

Don't get discouraged.. its natural to get bogged down by all these counting problems (some can really make your head swim!). You get better with practice! These are the fundamentals of counting so there really isn't any other math that will make it easier. Last edited:
Ok, so I must start posting jillions of problems to this forum; to get help from experts.
Thank you.

I will answer one of your question... which one you like? pick one...