Question

In a certain state, license plates consist of three letters followed by three numbers.

Answer 1

a. If any letters and numbers are allowed, there will be

... 26×26×26×10×10×10 = 260³ = 17,576,000 possible plates

b. If the letters and numbers cannot repeat, there will be

... 26×25×24×10×9×8 = 11,232,000 possible plates with no repeats

c. The proabaility that a randomly chosen plate has no repeats is

... 11,232,000/17,576,000 = 108/169 ≈ 0,63905

_____

When no repeats are allowed, the first letter choice can be any of the 26 letters. The second letter choice must exclude the first letter, so there are only 25 different letters to choose from. Likewise, the third letter choice cannot be either of the first two, so there are only 24 letters to choose from. The reasoning applies to numbers in similar fashion.