There are times when the sample space or event space are very large, that it isn’t feasible to write it out. In that case, it helps to have mathematical tools for counting the size of the sample space and event space. These tools are known as counting techniques.
In Example , the solution was found by find . Many counting problems involve multiplying a list of decreasing numbers. This is called a factorial. There is a special symbol for this and a special button on your calculator.
As an example:
0 factorial is defined to be 0!=1 and 1 factorial is defined to be 1!=1.
Sometimes you are trying to select r objects from n total objects. The number of ways to do this depends on if the order you choose the r objects matters or if it doesn’t. As an example if you are trying to call a person on the phone, you have to have their number in the right order. Otherwise, you call someone you didn’t mean to. In this case, the order of the numbers matters. If however you were picking random numbers for the lottery, it doesn’t matter which number you pick first. As long as you have the same numbers that the lottery people pick, you win. In this case the order doesn’t matter. A permutation is an arrangement of items with a specific order. You use permutations to count items when the order matters. When the order doesn’t matter you use combinations. A combination is an arrangement of items when order is not important. When you do a counting problem, the first thing you should ask yourself is “does order matter?”
Most calculators have a factorial button on them, and many have the combination and permutation functions also. R has a combination command.
