Give a real-world example of how permutations and combinations can be used. Explain what your numeric result means in context of the real-world application.

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A very simple example of combinations would be in the number of pizzas one could create given a certain number of criteria. In other word, given that a pizza place has:

3 types of crust -thin, regular,  thick

4 types of toppings - pepperoni, sausage, ham, bacon

3 types of cheese - American, cheddar, Swiss

How many different one topping, one cheese pizzas could be made?? Answer - multiply them all together because the order of choice does not matter here, so 3*4*3 =36

An example of permutations would be the arrangement of books on a shelf. An easy one is to say there are 5 different books...how many ways can you arrange them on the shelf (in the typical upright position of libraries) ?? Answer - then you have 5 choices for the first book, 4 choices for the second (because you cannot use the one you have already placed on the shelf), 3 choices, etc. So multiply 5*4*3*2*1 = 120 ways. Now you can see why the chances of winning a lottery can be so slim. (Consider the number of ways you can arrange ten (0-9) digits in a given number of slots.)

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