What is the difference between a combination and a permutation?
Permutation: A set of objects in which position (or order) is
Combination: A set of objects in which position (or order) is NOT
Put simply,a combination is just a collection of objects and permutations are different ways of arranging that combination.To show this ---
I can have a combination of 4 people on a commitee,say Art, Bert,Chas and Dave.
I could have picked this same commitee in 24 different ways ( that is 24 permutations)
To show a few,so you get the idea,I could have picked
Chas,Dave,Bert,Art (I'm not listing all 24 of them!) ,all of which gives me the same combination,but just permuted in different ways.
If I have a combination of 4 objects,the number of permutations of that combination is 24. Why?
-the number of choices I have for my first pick is 4. Now I only have 3 choices left for my next pick,and at this stage ,with every one of my 4 picks,I have a choice of 3 picks ie 4 x 3. After my 3rd pick,I only have 2 choices left, so now I have 4x3x2 permutations and finally only one left, we usually include the 1 to write 4x3x2x1.