Question

6. A certain state has license plates showing three numbers and three (upper case) letters. How many different license plates are possible (a) if the numbers must come before the letters? b) if there is no restriction on where the letters and numbers appear?

Answer 1

Solution:

Number of English Alphabets (A-Z) = 26 , & number count (0-9) = 10

(a) if numbers come before letters =   $\frac{_{3}^{10}\textrm{P} * _{3}^{26}\textrm{P}}{ _{1}^{2}\textrm{P}}$ = (720 * 15600)/ 2 = 56,16,000

(b) No restrictions:

sol (a) * 2 = 11,232,000