STATS question

Question

The access code for a car's security system consists of six digits. The first digit cannot be 5 and the last digit must be odd. how many different codes are available?

Answer 1

Hi Deion.  Let's tackle this digit by digit.

 

You didn't say anything so I have to assume that other than the two conditions mentioned for the fist and last digit, all numbers 0-9 are permissible.

 

1st digit cannot be a 5.  Therefore there are 9 possibilities

digits 2-5 can be any digit.  There are 10 possibilities for each.  There are 4 digits involved, so there are 10⁴ possibilities.

Finally the last, 6th digit must be odd.  Therefore there are 5 possibilities.

 

The number of different possible codes is

9 x 10⁴ x 5 = 45 x 10⁴ = 450,000