A password consists of two letters of the alphabet followed by 4 digits chosen from 0 to 9. Repeats are not allowed. How many possible passwords can be created?

Question

A password consists of two letters of the alphabet followed by 4 digits chosen from 0 to 9. Repeats are not allowed. How many possible passwords can be created?

Answer 1

I assume that there is no difference between upper case and lower case letters

2 letters can be chosen from the 26 available in 26C2 ways, calculated as 26!/(2!)(24!) = 26*25/2*1 = 325

4 numbers can be chosen from the 10 available in 10C4 ways, calculated as 10!/(4!)(6!) = 10*9*8*7/4*3*2*1 = 210.

The number of passwords is then 325 * 210 = 68,250