Question

Can someone give me a clear picture of the working between permutations and combinations? I've learnt how to approach the questions but I can't seem to differentiate between the two at times. I'll need help on this.

Answer 1

Could you give a specific example of each (they are quite similar and I'm not sure I see the difference?)

Answer 2

When you just have to find the number of ways you could pick out some number of objects from the whole, you use COMBINATIONS.

When you want to find the number of ways you could pick out some number of objects from the whole, AND THEN PUT THEM IN DIFFERENT ORDERS, you use PERMUTATIONS.

Answer 3

The number of ways you can pick out 3 objects from 5 is \(5C3\).
The number of ways you can arrange 3 objects out of 5 is \(5 P3\).

Answer 4

Does that help?

Answer 5

@barrycarter:
James has to play 4 songs from a list of 7 songs. Of these 7 songs, 4 were written by Beethoven and 3 songs were written by Mozart.
Fine the number of ways the 4 songs can be chosen if
(a) there are no restriction
(b) there must be 2 songs selected from each composer

@ParthKohli:
Let me read your statements first while I post up the question for barry to have a look as an example.

Answer 6

@Japorized Since you're choosing 4 songs without regard to order, that's a combination. If you had to choose the 4 in order, and "ABCD" was different from "BACD", that would be a permutation

Answer 7

But for case (b), according to what's given as a sample answer, they used permutation. But it requires no arrangement.

Answer 8

@Parth: I know this concept but sometimes, the thing is that when the question comes up, these key words aren't mentioned or implied. That's what makes me indecisive between the two,

Answer 9

Sorry, wrong tagging. :P
@ParthKohli

Answer 10

Another important thing to know is that the number of combinations ≤ number of permutations. Once you have your selection of things, there can be several different ways to arrange them.
This can be seen in the formulas.
\[nPk=\frac{n!}{(n-k)!}; \space nCk=\frac{n!}{k!(n-k)!} \space .\]
The formulas are identical except that nCk divides out the number of equivalent permutations which contain the same items.

Answer 11

I've referred to some references around and found one important thing.
Permutation emphasizes on arrangement.
Combination does not emphasize on arrangement at all.

Thanks for all the formulae but that's not what I want cause even if I have them, I can't use them without recognizing my question as a permutation question or combination question.