Permutation and Combination

In summary, the author thinks that it is important to learn the basics of probability in order to move on to more difficult problems. He thinks that there is no other math that will make it easier.
  • #1
Omid
182
0
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 learned 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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  • #2
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! :biggrin:

These are the fundamentals of counting so there really isn't any other math that will make it easier. :frown:
 
Last edited:
  • #3
Ok, so I must start posting jillions of problems to this forum; to get help from experts.
Thank you.
 
  • #4
I will answer one of your question... which one you like? pick one...
 
  • #5
The third one please.
 

1. What is the difference between permutation and combination?

Permutation and combination are both ways of arranging a set of objects or elements. The main difference is that permutation considers the order of the elements, while combination does not. In other words, with permutation, the order matters, while with combination, it does not.

2. How do you calculate the number of permutations?

The formula for calculating permutations is n!/(n-r)!, where n is the total number of objects and r is the number of objects in each permutation. For example, if you have 5 objects and want to find all possible permutations of 3 objects, the calculation would be 5!/(5-3)! = 5! / 2! = 120 / 2 = 60 permutations.

3. How do you calculate the number of combinations?

The formula for calculating combinations is n!/r!(n-r)!, where n is the total number of objects and r is the number of objects in each combination. For example, if you have 5 objects and want to find all possible combinations of 3 objects, the calculation would be 5!/(3!(5-3)!) = 5!/(3!2!) = 120 / 6 = 20 combinations.

4. What is the difference between with replacement and without replacement in permutation and combination?

With replacement means that an object can be chosen more than once in a permutation or combination, while without replacement means that once an object is chosen, it cannot be chosen again. For example, when drawing cards from a deck, with replacement means that a card can be put back into the deck and drawn again, while without replacement means that once a card is drawn, it cannot be drawn again.

5. How are permutation and combination used in real life?

Permutation and combination are used in a variety of fields, including mathematics, statistics, computer science, and engineering. In real life, they can be used to calculate the number of ways a group of people can be seated at a table, the number of possible outcomes in a game, or the number of possible combinations in a lock. They are also used in probability and statistics to analyze data and make predictions.

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