A state had three letters followed by three digits as the format for license plates. In order to increase the number of plates available, the state changed the format to four letters followed by two digits. What is the positive difference between the number of plates available with the new format and the number of plates available with the old format?

Guest Jun 28, 2019

#2**+2 **

There are 26 different letters and 10 different digits.

number of possibilities with 3 letters and 3 digits = 26^{3} * 10^{3}

number of possibilities with 4 letters and 2 digits = 26^{4} * 10^{2}

the positive difference between them = 26^{4} * 10^{2} - 26^{3} * 10^{3}

the positive difference between them = 26^{3} * 10^{2} * (26 - 10)

the positive difference between them = 26^{3} * 10^{2} * 16

the positive difference between them = 28121600

hectictar Jun 29, 2019