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?

Answer 1

It's a Permutation of 9 digits chosen out of 10 digits with no repeat:

¹⁰P₉ = (10!)/(10-9)! = 3,628,800 cards

Answer 2

10*9*8*7*6*5*4*3*2*1

Considering that when you use a digit you can't use it again, the possibilities of a number filling a specific position is one less than before because the number was already used.

Using this the answer should be
3,628,800