Question

Access code for a car security system consist of six digits. The first digit cannot be nine and the last digit must be odd. How many different codes are available. Note that zero is considered an even number.

Answer 1

Here the access code consist of Six digits from 0,1,2,3,4,5,6,7,8,9.

Now , the first digit cannot be nine, so the possible digits for 1st position are 9 i.e 0,1,2,3,4,5,6,7,8. The the 1st position(digit) is selected in 9 ways.

Similarly, the possible digits for 2nd position are 10 i.e 0,1,2,3,4,5,6,7,8,9. so the 2nd position(digit) is selected in 10 ways.

and

The possible digits for 3rd position are 10 i.e 0,1,2,3,4,5,6,7,8,9. so the 3rd position(digit) is selected in 10 ways.

and

The possible digits for 4th position are 10 i.e 0,1,2,3,4,5,6,7,8,9. so the 4th position(digit) is selected in 10 ways.

and

The possible digits for 5th position are 10 i.e 0,1,2,3,4,5,6,7,8,9. so the 5th position(digit) is selected in 10 ways.

and

The last digit must be odd ,so the last digit for the code has 5 possible digits i.e 1,3,5,7,9. The last digit is selected in 5 ways.

So the possible different codes are