Are you saying that the answers given are 10, 6 and 41?
If you are happy with 60 (5*4*3) as total permutations (order does matter) then try the following:
Each permutation of a, b, c can be written in 6 different ways (a, c, b etc). Therefore to get the total combinations you need to divide 60 by 6 to get rid of the repeats, leaving 10.
Do the same with chocolate start - 1 x 4 x 3 = 12 , divide by 2 combinations of the second two scoops = 6
My solution to part c - total variations including multiple of the same flavour:
10 different ways to have 3 different flavours
5 different ways to have all the same flavour
20 ways to have 2 scoops the same and one diff (4 different ways to have 2 scoops of chocolate and one other, multiply by the 5 flavours you could have two scoops of)
Total: 35.
I don't know what the other 6 are..... The part b answer (6) is included in part a.
this webiste seems to agree with me
35 as an answer I'm guessing I'm mis interpreting something
Edited by PatG, 11 February 2013 - 07:53 PM.