Answer:
A. 175,760,000
B. 156,000,000
Step-by-step explanation:
For part A:
There are 26 letters in the alphabet. Therefore, if there are 3 spots to use 26 letters, that is represented as [tex]26^3[/tex]. As for numbers, there are 10 digits from 0-9. So if there are 4 spots for numbers, the total possible number of sequences is [tex]10^4[/tex]. So you simply multiply [tex]26^3[/tex] and [tex]10^4[/tex] to get 175,760,000 possible combinations.
For part B:
If the same letter can't be repeated, instead of using an exponent, we have to use a factorial, but only for the 3 digits required in the license plate. These are called permutations and can be expressed as [tex]_2_6P_3[/tex], which is the same as saying 26 x 25 x 24. Since there is no change to number of numbers, that remains the same.
[tex]_2_6P_3 * 10^4 =26*25*24*10^4=156,000,000[/tex]
