If I am given the numbers 1-5, how do determine all the possible 4 digit combinations?

Question

I have a niece with a homework problem. If given the numbers 1, 2,3,4, and 5, how does she calculate or determine all the possible 4 digit combinations.

Answer 1

5 to the fourth power. 5 * 5 * 5 * 5 = 625

Suppose it was only one digit. Clearly there would be 5 different values, right?
Now suppose there were two. For each of the 5 possible first digits, there are 5 possible second digits. So 5 * 5 = 25
Now suppose there were three. For each of the 25 previous possibilities, you could have 5 possible first digits. 25 * 5 = 125.

You get the idea :-)

Answer 2

Theres a formula for "combination" problems. It's called "n-Choose-r"

If you have n numbers choose r of them and the number of combinations are.... etc.

You also need to know what a "factorial" is.
4 factorial is written 4! and it equals 4*3*2*1
6! is 6*5*4*3*2*1 etc.

So in this case it's 5choose4 and the formula is:

[5!] / [(4!) * (5 - 4)!]
= [5!] / [(4!) * (1!)]
=[5*4*3*2*1] / [(4*3*2*1)*(1)]
=120 / 24 = 5

5 possible combinations

Answer 3

If you want the actual combinations, you'll just have to crank them out, do them in order so you're sure not to omit any. If you just want to know how many combinations there are, think of 5 playing cards. You've got 5 ways of picking the first card, it could be a 1 or 2 or 3 or 4 or 5. Then you have to pick a second card, but you now only have 4 options as to which one it might be, but you've got each of those 4 options for each of the 5 cards you picked for the first card. Replicate this pattern for all 4 cards. Mathematically, this is represented as 5*4*3*2=120
5432

Answer 4

It depends on if there is repetition or not. If you can repeat the numbers then you would use 5*5*5*5*5. If you can't repeat the numbers then you would use the 5*4*3*2*1. This is because repetition meanse that numbers repeat meaning there are five possibilities in each digit, if there is no repititon then is means that the possibilities go down with each digit, resulting in the 54321.

Answer 5

five to the fourth power.

Say you have two digits. Each second digit matched with each first digit has five combinations, e.g., for one, you have 11, 12, ..., 15. There are five such second digits, so that's 5*5 combinations, or five to the second power. Each of these combinations, in turn, has five combinations with a third digits, or 5*5*5 = five to the 3rd power.

Answer 6

5 * 5 * 5 * 5 = 625

Answer 7

I believe it is a permutation question. Do this equation to get the answer 5x4x3x2x1= That should do it. good luck!

Answer 8

Multiply 5x4x3x2x1 and that will give you the answer.