Question

A license plate has 7 characters. Each character can be a capital letter or a digit except for 0. How many license plates are there in which no character appears more than once and the first character is a digit?

a. 9 P(35, 6)
b. 9 P(34,6)
c. 9.(35)^6
d. 9.(35)^6

Answer 1

b. 9 P(34,6)

Step-by-step explanation:

Since the 1st character of the number plate is the digit, therefore, there are nine possible ways to select them from digits 1 to 9.

And in the license plate there are 7 characters, the first character is counted before and the remaining 6 characters that can either be a digit or a letter has to be considered.

Now there are in total 34 symbols remaining form a total of 26 letters and 8 digits. They can be placed as 34x33x32x31x30x29 ways = P(34, 6) ways.

Therefore in total for all the characters there are 9 x P(34, 6) different ways.