What is the formula to get 4 digit combinations from numbers 0-9? How do you calculate how many numbers?

Question

The numbers cannot repeat themselves. Can you list them?

Answer 1

this is basically how it goes

there are 9 ways to choose the first number,
9 ways to choose the 2nd one,
8 ways to choose the 3rd one,
and 7 ways to choose the 4th one. this is because the first number can't be 0, so there are 9 numbers to choose from, then the second one there are 10 numbers, but one has already been chosen, so another 9 to choose from, 8 ways for the 3rd, because 2 have been selected, and 7 for the fourth, because 3 have been selected.

so 9 * 9 * 8 * 7 = 4536

there are 4536 ways to get a 4 digit number with no repeating numbers. I really don't feel like listing them.

the person who posted the answer above mine is wrong, because as i said, the first number can't be 0.

Answer 2

The formula for combinations for C(n,r) where n is the number of objects you have and r is the number used for the combination is :
n!/(r!(n-r)!) (Exclamation mark means multiply from that number all the way down to 1)
While it looks a little confusing, here is how you would use it for your example:
C(10,4) = 10! / (4!6!) = 10*9*8*7*6*5*4*3*2*1/(4*3*2*1 * 6*5*4*3*2*1)
Once you cancel terms from the top and bottom the equation always turns out to be r numbers on top and r numbers on bottom or in this case 4.
10*9*8*7/(4*3*2*1)
Now solve:
210 combinations

Answer 3

There are 10 digits in the sequence 0 - 9

If digits cannot be reused, the number of "permutations" is

10 X 9 X 8 X 7 = 5040

If order didn't matter, (i.e. if the number 3624 was considered a duplicate of 2643, 2346, etc, then the number of "combinations" would be

10 X 9 X 8 X 7 / 4 X 3 X 2 X 1 = 210

Sure, I can list them, but come on!

Answer 4

for each number past the first number you subtract 1 from the previous total possibilities then multiply the first total time the second time the third times the fourth.

In English 10 * 9 * 8 * 7 = 5040 total possibilities with a four digit non-repeating combination.

Answer 5

You have ten digits to use, four at a time.
Number of permutations without repeats = 10!/(10-4)!
Note that this will allow a leading 0, e.g., 0123.

Answer 6

10^4 = 10,000