Question

tandard automobile license plates in a country display 1 numbers, followed by 2 letters, followed by 4 numbers. How many different standard plates are possible in this system? (Assume lead 0 is not allowed, but repetitions of letters and numbers are allowed.)

Answer 1

Answer:

39,917,124

Step-by-step explanation:

In order to solve this problem we must start by drawing a diagram of what the licence plates look like. (See Attached picture).

Now, each box in the picture will represent one digit of the plate. Some must be numbers and some must be letters. We know we have 9 posibilities for theh numbered boxes (1-9) and we have 26 possibilities for the boxes that are to contain letters. Repetitions allowed. So the possible character for each box is as follows:

box 1 = 1 to 9 = 9

box 2 = A to Z = 26

box 3 = A to Z = 26

box 4 = 1 to 9 = 9

box 5 = 1 to 9 = 9

box 6 = 1 to 9 = 9

box 7 = 1 to 9 = 9

so the total number of licence plates can be found by multiplying the possibilities for each box in the plate so we get:

# of plates = (9)(26)(26)(9)(9)(9)(9)

which can be simplified to:

$plates= 9^{5}26^{2}=39,917,124$