How do you know when to use permutation or combination formula?

Question

Give an example of each

Answer 1

Hi funky,

Students have a lot of trouble with this.

A permutation is used when order is important.  

A combination is used when order is not important.

http://www.mathagonyaunt.co.uk/STATISTIC...

Try the above link or go to Google and type in key words permutation or combination for example.

Good luck to you !

Answer 2

A combination is used when you have a set of things and you take a subset of them. A classic example is having a deck of 52 cards and dealing a hand of 5 cards from it. You typically are interested in finding out how many different combinations of 5 cards you could draw from a shuffled deck. Another example would be ordering a pizza which can have 10 different toppings of which you can pick 3, how many different pizzas could you make? The function that calculates the number of combinations of "n" items taken in subsets of "r" items is often written nCr. In the case of the cards example you'd write 52C5 and for the pizza you'd write 10C3. You can find the equations for calculating nCr in the links below.

Permutations are how many different *orders* of items you can select from a set. This is usually written nPr where "n" and "r" have the same definition as for combinations. A fair example is there are three students named X, Y, and Z, how many different ways can you line them up? The permutations would be: XYZ, XZY, YXZ, YZX, ZXY, and ZYX. In this case the function would be written 3P3. Another example would be you want to go shopping (G), meet with friends (M), and do your homework (H), but you only have time for two of them. How many different ways could you do these in what order? You could do: GM, MG, GH, HG, MH, and HM. For this the function would be written 3P2

Answer 3

Use permutation when the order counts. Use combination when it doesn't. For example, let's say you have a bunch of different crayons and you pull out three.

red-yellow-blue

red-blue-yellow

yellow-red-blue

yellow-blue-red

blue-red-yellow

blue-yellow-red

These are all different possible permutations, but all six of these would only count as *one* possible combination (i.e., you have red, yellow, and blue, it doesn't matter what order you pulled them out).