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?

1 Answer
Shwetank Mauria
Jan 18, 2017

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

Explanation:

Number on license plates are of the form #LLLDD#, 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 #26xx26xx26=17576# combinations for letters.

But digits are from #0# to #9# i.e. #10# combinations for each place and tolal #10xx10=100# combinations.

Hence for #LLLDD#, we have #1,757,600# combinations available for license plates.

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