Babies born in the United States must have a Social Security card issued before their third birthday. How many different cards could be issued using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, if each card needs a nine-digit number and the digits can only be used once per card?

The formula is

n!
------
(n-r)!

Question

Babies born in the United States must have a Social Security card issued before their third birthday. How many different cards could be issued using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, if each card needs a nine-digit number and the digits can only be used once per card?

The formula is

n!
------
(n-r)!

anonymous · Answer

Each number has 10 choices. Since we don't have to worry about not using a number over and over, it will just be 10^9 or 10 times itself 9 times.

anonymous · Answer

says digits can only be used once

anonymous · Answer

so there are very few, namely $\binom{10}{9}=10$

agent0smith · Answer

@satellite73 I don't think that's right.

The first number has 10 available choices, the next 9, then 8, and so on.
10*9*8*7*6*5*4*3*2

agent0smith · Answer

Order matters, it's a permutation.

10P9