# 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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$26 \times 25 \times 24 = 15600$
We still have ${10}^{4}$ for the numbers, and so in total we have:
$15600 \times 10000 = 156 , 000 , 000$ plates