A frozen yogurt shop offers 10 different flavors of yogurt and 15 different toppings. How many double-dip sundae combinations can be created with 1 topping? One yogurt flavor may be used for both dips.

Question

anonymous · Answer

can a double dip have the same flavor twice?

anonymous · Answer

Both dips? Your questions seems to be skimping on some details, but if i'm reading this I'm guessing you mean that there's 10 different flavors of ice cream, how many combinations of 2 can you have, with repeating pairs. The answer would end up being 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1, or 55. Starting with flavor A, you have 10 combinations of flavors. Once moving to Flavor B, you've eliminated the option "AB", and you'd have 9 options. Travel down until you're done.

anonymous · Answer

You could think of your 10 flavors as 1 2 3 4 5 6 7 8 9 and 0. Your 55 options for flavors would then be 
11 12 13 14 15 16 17 18 19 10 22 23 24 25 26 27 28 29 20 33 34 35 36 37 38 39 30 44 45 46 47 48 49 40 55 56 57 58 59 50 66 67 68 69 60 77 78 79 70 88 89 80 99 90 00