Question

You bought six numbers at you local hardware store. The numbers are 0, 1, 2, 3, 4, 5.

a) How many 4 digit house numbers can you form using these numbers?
(note: 0351 is not considered a house number).

b) How many 4 digit house numbers are even?
(note: 0351 is not considered a house number).

Answer 1

the hint is a) is telling you the first number cannot be zero

Answer 2

so you have 5 choices for the first number, not six
then 5 for the second, 4 for the third, and finally 3 for the fourth
multiply to get your answer

Answer 3

so do I assume that i can't have a number repeating?

Answer 4

yes

Answer 5

Ya that seems correct.
It looks like, based on the wording, that you purchased one of each number, not an infinite amount of them to use.

Answer 6

For the first question, I believe the answer is 300, and here is why:

For the first digit, there are 5 possibilities: 1, 2, 3, 4, 5. For the second digit, there are again 5 possibilities, because we have 4 possibilities left over from the 1 through 5 set, plus 0. So that gives:

5 * 5

For the third number, we have four numbers left to choose from, because 2 of the 6 have been used, so we get:

5 * 5 * 4

Then the last digit has 3 possibilities, giving a final answer of:

5 * 5 * 4 * 3 = 25 * 12 = 300.

I will let someone else do the second problem :-).