Please help me find a solution to this problem 
Blue-Bunny Ice Cream, sells 31 flavors.
A.) How many 2-dip cones are possible if order of flavors is to be considered
and no flavor is repeated?

Choose the bottom dip 31 ways. For every one of these you may choose
the top dip 30 ways.  That's 31·30 or 930 ways.  That counts, for instance,
vanilla on the bottom and chocolate on top as a separate cone from
chocolate on the bottom and vanilla on top. 

B.) How many 2-dip cones are possible if order of flavors is to be considered
and flavors CAN be repeated.

This is a difficult problem.  This involves advanced combinatorics.
I don't think your teacher or textbook author should expect you to be able to
do this one because it involves a summation over all the ways you can have
k repeated flavors and 31-k non-repeated flavors for 0 < k < 31.  I think 
your teacher and/or the textbook author may have thought this to be an easier
problem than it really is. 

C.) How many 2-dip cones are possible if order is NOT considered 
and NO flavor is repeated?

This is the combinations of 31 things taken 2 at a time:
                        15
           31·30     31·30
C(31,2) = ------- = ------- = 31·15 = 465
            1·2       1·2
                        1  

Edwin