We have five cards, a square, a triangle, a star, a circle and three wavy lines. We choose one card at random and place it on a table. We then choose a second card and place that next to the first, and so on until we have all five cards on the table.
There are five ways of choosing the first card, four for the second, etc, so the total number of permutations is 5×4×3×2×1 or 120. We call this number five factorial, and write it as 5! There is a factorial key (x!) on your calculator: to find 7! enter 
Try it, the answer should be 5040
If we draw only two cards from the five there are only 5×4 or 20 combinations. We can easily show that this is 
In general terms, if we have n objects and draw out r of them the number of permutations is 
We write this as nPr. There is an nPr key on your calculator. To find 8P5 you enter
Sometimes we need not the number of permutations but the number of combinations, where the order does not matter, for example there are six permutations of a square a triangle and a star but if the order does not matter there is only one combination. The number of combinations is given the symbol nCr and we can show that it is 
We use the nCr key in exactly the same way as the nPr key.
See if you can work out 59C6 (the chance of winning the National Lottery!)
Your calculator needs to do a lot of sums when working out factorials, permutations and combinations, so do not expect instant results.
