Ranking...?

Question

If I have 4 things that need to be ranked in different orders, like ABCD, or ADBC, how many options are there for different rankings?

Is there a formula to figure this out?

Answer 1

this is a probability statement. Basically, multiply each of your possible options together. When you start off, you have 4 letters.

One of these 4 letters has to go into the first position, that leaves 4 possibilities.

4

Now for the next slot, you only have 3 possibilities left. Remember though, that you have these 3 possibilities for every single one of the 4 possibilities you started out with.

4x3

now you only have 2 possibilities left for the last slot, and so on.

4x3x2x1

If you didn't have to put them in order, and you could use each letter over again for each slot, then you would have 4 possibilities for each slot instead of them decreasing by 1 each time, and it would look like this instead:

4x4x4x4

On a similar note, if you had 5 letters (A B C D E) and only 3 different slots to put them in, it would look like this:

5x4x3

because you have 5 possibilities for the first slot, 4 for the next, 3 for the next, and then you run out of slots. Again, if you could re-use letters that you already used before, it would look like this instead:

5x5x5

Answer 2

Yes, you have 4 choices for the first rank.
3 choices for the second rank, 2 choices for the third.
So the answer is: 4 x 3 x 2 x 1 = 24
Now you know how those lotteries figure the odds.

Answer 3

If all 4 numbers are different! then 4x3x2x1=24 more easily written as 4 factorial or simply "4!"
find formluas in 2nd yr algebra book!

Answer 4

Not sure whether this is "permutations" (which I think it is), or "combinations" (which it might be, instead), but you could type these words into your favorite search engine. I bet you'd hit something that explains and gives the formulas.

For a small group like the one you mention, I'd just count them up, myself.

Answer 5

in a graphing calculator go to math/prob/and find the "!"
once you do that put the number of variables you have then the "1"
hit enter and there is your answer.
now you dont have to go on here to do your math homework.