Question

A license plate consists of 4 capital letters followed directly by 3 digits. How many plates are there which does not have 2 and G in it? Example: Cannot be AIDG352, but it can be GGGG134 or EOSL2222.

Answer 1

The license plate consists of 4 capital letters followed directly by 3 digits.

We have to calculate how many such plates are there which does not have 2 and G in it.

There are a total of 7 spots to be filled in which the first four are capital letters and the remaining three are digits.

The first four spots have 25 choices (after G excluded) and number of ways in which these four spots are arranged is .

The remaining three digits have 9 choices (after 2 excluded) and the number of ways in which these three spots are arranged is .

total number of plates in which they does not have 2 and G in it

Required number of plates= 284,765,625