Question

1. An island is considering adding another character to their vehicle license plates in order to increase thenumber of license plates available. Currently, a license plate must have exactly four-character spaces. Eachcharacter space may be filled with any capital letter other than I, B, Z, or 0 or any number between, andincluding, o to 9. Letters and numbers may repeat on the plates.(a) How many different license plate numbers are available under the current structure of exactly fourcharacters per plate? Show your calculations.(a) If the state required all license plates to have exactly five characters instead of four, how manydifferent license plate numbers would be available with the additional character requirement? Showyour calculations(a) How many times bigger is the set of license plate numbers with exactly five characters than that withthe set of four characters? Show your calculations.

Answer 1

We have a total of 26 letters and 10 algarisms.

After removing the letters I, B, Z and O, we will have 22 letters and 10 algarisms, therefore 32 options for each space.

a)

In order to find the number of licence plates available, we just need to multiply the number of possibilities for each space, so we have:

$32\cdot32\cdot32\cdot32=1048576$

b)

Since we have one more space, we just need to multiply the previous result by 32 again:

$1048576\cdot32=33554432$

c)

Dividing the values, we have:

$\frac{33554432}{1048576}=32$