Question

a realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of six digits. The first digit cannot be 3 and the last digit must be even. How many different codes are available? (Note that is 0 is considered an even number.)The number of different codes available is __(Type a whole number)

Answer 1

Notice that the first one of the 6 digits cannot be 3, so we are left in that case with only 9 digits to pick from for the first option.

The last digit must be even, so we are left with just 5 possible digits (0, 2, 4, 6, 8) for the last option.

So now we build the total number of combination using the fact that the four middle digits can be any of the 10 available digits:

9 * 10 * 10 * 10 * 10 * 5 = 450000 possible combinations.