Show all of the possible three-digit numbers with distinct digest that can be made using the digits 4, 5, 6, 5, an 7.

Yes I believe you are correct annon.

I guess I need new glasses.  LOL

The second 5 appears to be irrelevent.

So you want 3 digit numbers using   4,5,6 and 7

There are 4 choices for the first digit, 3 for the second and 2 for the third - that makes

4*3*2=24

just as anon said :))

There are 108 possible ways

I assume you mean.  How many distict 5 digit numbers can be made with the digits 4,5,5,6,and 7

Well, for the first digit there are 5 numbers to choose from.

for the second there are 4 numbers and so on so this is

5*4*3*2*1 ways  = 120 ways

However,  there are 2 5's so there are really half this number because, for instance, 

45567 is the same as 45567

so there will be  120/2 = 60 ways.

the more general formula for this is   5!/2!

The question asks for three digit numbers with distinct digits, (which I take to mean that we can't use both fives, and in which case the second five is irrelevant).

In that case, there will be 4 choices for the first digit, 3 choices for the second and 2 choices for the third.

24 possible numbers.