Multiply the number of possible license plates for each county by the number of counties.
A
a
260 000
B
b
23 920 000
Practice makes perfect
a
We are told that a license plate has a two-digit number fixed by county, then one letter, and then four one-digit numbers.
We will find how many different plates are possible in each county. Let's first note some important things we can conclude from the given information.
The county code is fixed, so we have no options to select here.
There are 26 letters, so we have 26 options.
Finally, for the last four one-digits we have no restrictions. Since there are 10 digits in total, we have 10 ways to select the first digit, 10 ways to select the second one, and so on.
Therefore, we can use the Multiplication Counting Principle to find the number of possible license plates. It means we have to multiply the number of possible ways to select the letter by the number of possibilities for each of the last four digits. Let's do it!
26* 10* 10* 10* 10=260 000
Therefore, there are 260 000 different possible license plates for each county.
b
Given that there are 92 possible counties, we are asked how many license plates are possible in the entire state. Recall that there are 260 000 different possible license plates for each county. We can find the number of possible license plates for the entire state by multiplying these two values.
92* 260 000=23 920 000
Therefore, there are 23 920 000 different possible license plates for the entire state.
