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). Note use Permutations and combinations!

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) Example: L-000

For the letter, there are 5 choices; for the first digit there are 10 choices; for the second there are 10 choices; and for the third, there are 10 choices as well.

5*10*10*10 = 5,000

(2) For the letter, there are 5 choices; for the first digit there are 10 choices; for the second digit there are 9 choices; for the third digit there are 8 choices. That can also be 5 times the permutation 10 taken 3 at a time.

5 * ₁₀P₃ = 5* (10*9*8) = 3,600