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# A license plate composed of $3$ letters followed by $4$ digits. How many different license plates are possible?

Last updated date: 20th Jun 2024
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Hint: In this problem we need to calculate the number of different license plates possible for the given condition. In the problem they have mentioned that the plate consists of $3$ letters followed by $4$ digits. So first we will calculate the number of ways to choose $3$ letters from the number of letters we have which is $26$. Now we will calculate the number of ways to choose $4$ digits from the number of digits we have which is $10$. After calculating the number of ways to choose letters and digits we will multiply them together to get the required result.

Complete step by step solution:
Given that, A license plate composed of $3$ letters followed by $4$ digits.
First considering the letters in the plate.
The plate consists of $3$ letters. We have $26$ letters which start from A to Z. So, we can choose $3$ letters from $26$ letters in ${{26}^{3}}$ ways.
Considering the digits in the plate.
The plate consists of $4$ digits. We have $10$ digits which starts from $0$ to $9$. So, we can choose $4$ digits from $10$ digits in ${{10}^{4}}$ ways.
Hence the number of possible plates is ${{26}^{3}}\times {{10}^{4}}=17,57,60,000$.

Note:
Generally, we can see that the letters and digits in the number plates are repeated, so we have not considered the reputation. If they have mentioned that the reputation is not allowed in the problem, then we will go to the concept of permutations and combinations.