What is the difference between combinations and permutations?

What is the difference between combinations and permutations? Give details

Solutions

Expert Solution

Let's say you choose a committee of three to represent your class of 30 students:

For the first member you have

30 choices

For the second you have

For the third you have

For a total of 30⋅29⋅28=24360 possible permutations

Now this is assuming that the order of choice is relevant: the first one will be called 'president', the second will be 'secretary' and the third will be just 'member'.

If this is not the case (all three are equal) then the order in which they are picked is not important.

With three picked there are 3⋅2⋅1

=3!=6

possible orders, which all give the same group. These are called combinations .

So: combinations= permutations divided by orders

Or, in our example:

24360/6=4060

It depends of whether the order is important.

Sankar Maity answered 1 year ago

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