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?

Answer 1

The number of possible license plates will be;

8,714,977,920

Explanation:

The number of digits is 1-9 making 9

The number of alphabets is A-Z making a total 26

Number of characters is 26 + 9 = 35

Now for the 1st character

we have 9 choices

Second character, we have 34 choices since no character appear more than once

Third character, we have 33 choices

fourth 32 choices

fifth 31 choices

sixth 30 choices

seventh 29 choices

Number of possible license plates will be;

9 * 34 * 33 * 32 * 31 * 30 * 29 = 8,714,977,920