Question

How many different license plates involving three letters and two digits are
there if the three letters appear together either at the beginning or end of the
license?

Answer 1

Answer:

${\boxed {\boxed{351,520,000{ {\ }}}}}$

Step-by-step explanation:

Let us consider the letter portion of the plate

Each of the 3 letters have 26 choices and note that letters can be repetitive, for example AAP, BBB, XYX, etc, on licence plate.

So we have $26^3$ permutations/ways of forming letters of plate

on the same lines we can have (10)^4 ways of forming number portion as there are 4 digits and each digit can be any of 0 to 9, including the first digit

For each of the 26^3 arrangements of letters we have 10^4 arrangement of numbers

Also the letter portion can appear in beginning or at end.

So the total number of different license plates = $2(26^3)(10^4)$ = 351,520,000

${\boxed {\boxed{351,520,000{ {\ }}}}}$