Question

The access code for a car's security system consists of 4 numbers. The first digit cannot be a 6 and the last digit can not be odd. How may different codes are available?

Answer 1

For 4 numbers, there are 10^4 (10 because of 0-9 and the power of 4 because there are 4 digits) possibilities, or 10000 (10x10x10x10) Now the restrictions come in: Since the first digit cannot be one possibility, we knock the first 10-multiple to 9: (9x10x10x10)
Now for the last digit, there are, from 0 to 9, 5 odd numbers (1,3,5,7,9), so the last digit only has 5 possibilities, so substitute the final 10 for 5: (9x10x10x5)
Multiply this out and you will know how many different codes are possible.

Answer 2

Thanks

Answer 3

Not only did you provide the answer but you gave an explanation. I beleive I can tackle probelms like this one.