Probability, chose two skittles, out of 2 skittles left from a bag of skittles with 5 colors. so me and my friend are studying statistics but we are just stuck on this stupid skittle question we made up ourselves when we tried to guess the colors of the two last skittles so we can see who will eat them. So out of a bag of skittles we had 2 skittles left, and there are 5 colors. I guessed red and purple, my friend guesses green and yellow. It turned out that the two skittles were red and purple so I won. After much debate we figured out my hand that there can only be 15 different outcomes such as red,red, green,green, yellow,yellow, purple,purple, orange,orange, red,purple red,yellow and so on..... What is the actual steps and formula for this? We are stuck at uni studying for so long we can't even solve this simple question ;( Thank you in advanced for the help.

This is a multiset problem. So the count is $$\binom{colors + skittles - 1}{skittles}$$

So we have $5$ colors and $2$ skittles, so we get $\binom{5 + 2 - 1}{2} = \binom{6}{2} = 15$.