Question

The access code for a home security system includes of

six numbers and the 1st # is not

thirty three

and the last number is odd. How many different codes are there? Also, 0 will be thought of as an even number.

The number of different codes available is what

I need help understanding how to do this problem etc.

Thanks.

Answer 1

The home security system includes 6 numbers

_ _ _ _ _ _

The first two places can have any number except 3 3

Thus the first place can be filled in 9 ways ( 0,1,2,4,5,6,7,8,9)

The second place can be filled in 9 ways ( 0,1,2,4,5,6, 7,8,9)

The third place can be filled in 10 ways (0,1, 2, 3, 4,5, 6, 7, 8, 9)

The fourth place can also be filled in 10 was (0,1, 2, 3, 4,5, 6, 7, 8, 9)

The fifth place can alse be filled in 10 ways (0,1, 2, 3, 4,5, 6, 7, 8, 9)

The sixth place can be filled in 5 ways ( only odd numbers i.e, 1,3,5,7,9)

Thus the number of different codes available is = 9 * 9 * 10 * 10 * 10 * 5 = 405000