A certain state has license plates showing three numbers and three letters.
How many dierent license plates are possible
if there is no restriction on where the letters and numbers appear? the answer in my text says 6c3 * 10^3 * 26^3??

Question

A certain state has license plates showing three numbers and three letters.
How many dierent license plates are possible
if there is no restriction on where the letters and numbers appear? the answer in my text says 6c3 * 10^3 * 26^3??

anonymous · Answer

Okay, so there are three numbers and three letters. Basically, 

_ _ _ _ _ _

where each line represents a number or letter.

For three of them, with no restrictions, you can insert 0 - 9 in each of them. That is 10 possibilities for each. So, 10 * 10 * 10, which is indeed 10^3.

For the other three, you can insert A-Z or 26 possibilities in three spots. That is 26^3 possibilities. 

Finally, since they can be arranged in any order, and there is 6 possibilities of number-letter combinations (ex. NLN LNL, NNN LLL), this gives you your first number.