License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed?

Jan 18, 2017

We have $1 , 757 , 600$ combinations available for license plates.

Explanation:

Number on license plates are of the form $L L L D D$, where $L$ represents a letter and $D$ represents a digit.

As $L$ can be anything from $A$ to $Z$, there are $26$ combinations for that and as repetition is allowed,

for second and third letters, we again have $26$ combinations available and thus $26 \times 26 \times 26 = 17576$ combinations for letters.

But digits are from $0$ to $9$ i.e. $10$ combinations for each place and tolal $10 \times 10 = 100$ combinations.

Hence for $L L L D D$, we have $1 , 757 , 600$ combinations available for license plates.