Suppose there's a company that's making ID badges for its employees.

Question

Suppose there's a company that's making ID badges for its employees. IDs are made up of one vowel (A, E, I, O, U) and three numbers (0,1,2,3,4,5,6,7,8,9)

1.  what's the total number of badges that can be created?
2.  what's the total number of badges that can be created without repeating a number?

Answer 1

1.

There are 5 vowels and 4 positions it could be in, making 20 ways.

For the remaining 3 positions there are 10 digits available for each position, making 10³ ways

Multiply them all together: 20*10³ = 20000

2.

There are 5 vowels and 4 positions it could be in, making 20 ways.

For the remaining 3 positions there are 10 digits available for the first, 9 digits available for the second, and 8 digits available for the third.

Multiply them all together: 20*10*9*8 = 14400