Combinations and Permutations in ice cream cones... what is the difference? The first two I am certain I have correct however c and d... I am struggling to understand the difference. I have done research on this site and have seen similar questions with explanations but I just want to double check my thinking. 
A certain store sells 31 different flavors of ice cream.  How many different 3-scoop cones are possible if:
a. each flavor must be different and the order of the flavors is unimportant? $31 nCr 3 = 4495$
b. each flavor must be different and the order of the flavors is important? $31 nPr 3 = 26970$
c. Flavors need not be different and the order of the flavors is unimportant? (This is a nontrivial question.)
I think I need to use this formula $$\binom{n+m-1}{m}$$
where $n$ in the total numbers in the set, and m is how many numbers you want to choose.
So,  $$\binom{31+3-1}{3}=\binom{32}{3}=\frac{32\times 31\times 30}{1\times 2\times 3}=4960$$  Is this correct?
d. Flavors need not be different and the order of the flavors is important? 
I am thinking this is $31 \cdot 31 \cdot 31 = 29791$

part d) is correct
part c) should be:
all different: $\binom{31}3$
two the same: $31\times30$
all the same 31
total $5456$
