F.5 數學功課

1. In each of the following, find the number of 4-digit numbers that satisfy the
given condition.

(a) The units digit is an even number. (Ans:4500)
9*10*10*5 (first digit cannot be 0,last digit must be even)
=4500
(b) The thousands digit or the units digit is an even number. (Ans:6500)
4500+5*10*10*10-4*10*10*5-1*10*10*10 (ans of a + thousands digit even - both thousands and unit even - thousands unit is 0)
=6500



2. The licence pates of cars consist of 2 upper case letters followed by 4 digits,
in which the first digit cannot be '0'.

(a) If the letter ' I ' and ' O' cannot be used and the digits cannot be all the same, then how many different license plates are posible?24*24*10*10*10*9(<suppose thousands, hundreds and tenth unit are same number)
=5184000


3. Suppose each user on a computer system requires a password of 6
characters. Each character can be a lower case letter or a digit. If the
password must contain at least one digit, find the number of possble
passwords.
(26+10)^6-26^6 (all possible passwords without limitations - all digits are characters)
=1867866560(唔知有冇撳錯機