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

${26}^{3} \times {10}^{4} = 175 , 760 , 000$ plates

#### Explanation:

There are 3 spots where there are 26 choices each $\left(= {26}^{3}\right)$ and 4 spots where there are 10 choices each (the digits 0 through 9, $= {10}^{4}$). This gives:

${26}^{3} \times {10}^{4} = 175 , 760 , 000$ plates

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If the same letter can't be repeated, we can look at things this way. The first letter spot can be any one of the 26 letters. The second letter spot can be any one of the remaining 25 letters. And the third letter spot can be any one of the remaining 24 letters. This gives, for letters:

$26 \times 25 \times 24 = 15600$

(note - this is the same as a permutation with population 26 and picking 3)

We still have ${10}^{4}$ for the numbers, and so in total we have:

$15600 \times 10000 = 156 , 000 , 000$ plates