A license plate is to consist of 3 letters followed by two digits. how many different license plates are possible if the first letter must be a vowel (a,e,i,o,u) and repetition of letters is not permitted, but repetition of digits is permitted
Let's take a sample license plate
E U A 3 7 3
We can choose a letter to go where the E is in 5 ways.
For each of those 5 ways,
we can choose a letter to go where the U is in 4 ways.
That's 5x4 ways or 20 ways.
For each of those 5x4 or 20 ways,
we can choose a letter to go where the A is in 3 ways.
That's 5x4x3 ways or 60 ways.
For each of those 5x4x3 or 60 ways,
we can choose a digit to go where the first 3 is in 10 ways.
That's 5x4x3x10 ways or 600 ways.
For each of those 5x4x3x10 or 600 ways,
we can choose a digit to go where the 7 is in 10 ways.
That's 5x4x3x10x10 or 6000 ways.
For each of those 5x4x3x10x10 or 6000 ways,
we can choose a digit to go where the 3 on the right end
is in 10 ways.
That's 5x4x3x10x10x10 or 60000 ways.
That's the answer.
Edwin