What is the difference between combinations and permutations?

Feb 20, 2015

It depends of whether the order is important.

Example:
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 $29$
For the third you have $28$

For a total of $30 \cdot 29 \cdot 28 = 24360$ 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: $24360 / 6 = 4060$

GC:
You will find the functions $n P r$ and $n C r$
where -in this example- you would do
$30 n P r 3$ and $30 n C r 3$ respectively.
There is also a function called n!
And you will notice that: 30nPr3=3!*30nCr3