Permutation is pretty simple actually. Imagine that you have to make a 4 digit number with the numbers 124657 . And you cannot repeat the integers. Then, you simply do 6 per mutate 4, as there are 6 possible integers and you need to select four. The result would be 6*5*4*3, as there are four places.
You can apply this to several problems that also involve arrangement. Take a scenario in which you have some tiles, each 2 by 1 cm thick, and you have to make a 6cm long line. The first scenario would be in which the shorter ends of the tile, the breadth , are arranged side by side. The number of ways to do this would be
\frac{6!}{6!}=1
As you have 6 similar tiles and six slots. This is also a form of permutation. Now, let us take a slightly different arrangement. You take 4 breadths and one length( 4 one cm breadths, and a single two cm length will give you 6 cm). The number of ways would be
\frac{5!}{4!1!}=5
As you have a total of 5 tiles being used, and 4 breadths and 1 length. So, to find the total number of ways, you simply investigate every single possibility. Another arrangement would be 2 two cm sides and 2 one cm sides. As explained above, the number of ways would be
\frac{4!}{2!2!}=6
If you ask me how this is related to the simpler 5P2 permutation, well then it is very similar. 5P2 is basically
\frac{5!}{3!}
However, by representing it like how I did, you allow room for more than one factorial in the denominator. Permutation is more complex than combination because in permutation,placement matters, unlike combination, which is just pretty much taking something out of something. Permutation is rather useful as it removes lengthy tables and replaces them with pure math.
