AMDA WORK MUST BE SHOWN

Question

The rules for license plates in Idaho are 3 letters followed by 4 numbers (example ABC 1234), where the first letter can only be the letters I, D, A, H, or O. How many different license plates can there be?

Answer 1

For the letter combinations, since the first letter (of 3 total letter placements) is limited to only 5 different letters while the next two letter placements can have all 26 letters; therefore, the total letter combinations are equal to:

 

5 x 26 x 26 = 5 x 676 = 3380

 

For the number combinations, 10 numbers (0 - 9) for each of a total 4 number placements are equal to:

 

!0 x 10 x 10 x 10 = 10^4 = 10,000

 

Combining the letters and numbers,

 

3380 x 10,000 = 33,800,000 different license plates possible