A state's license plates consist of four letters followed by three numerals, and 246 letter arrangements are not allowed. How many plates can the state issue?
26^26^26^26=456976-246 answer 456,730
thank you
You have completed the first part of the correct answer, but you forgot the 3 numerals.
So
456730*10^3
You're almost there! However, there seems to be a small error in your calculation.
To find out how many plates the state can issue, we need to calculate the number of possible combinations. We can break it down into two parts: the letters and the numerals.
For the letters, there are 26 possibilities for each of the four positions. So the number of letter combinations will be: 26 × 26 × 26 × 26 = 26^4 = 456,976.
For the numerals, there are 10 possibilities for each of the three positions (0-9). So the number of numeral combinations will be: 10 × 10 × 10 = 10^3 = 1,000.
Since the letter combinations and the numeral combinations are independent of each other, we multiply them together to get the total number of plate combinations: 456,976 × 1,000 = 456,976,000.
So the state can issue 456,976,000 license plates.
Note: The given information about 246 letter arrangements not being allowed is not necessary to determine the total number of plates. It only affects the number of valid letter arrangements that can be used on the plates.