# Permutation/Combination problem - choosing 2 objects from different categories

Context: there are three candies in a basket (5 red, 4 blue, 5 green). How many ways can you choose 2 candies with different color?

Should I use permutation or combination w/ this? I tried using: 14!/(14-2)! = 182 ways; but it's marked as wrong.

You can choose $5\times4$ pairs of candies s.t. one of them is red and one of them is blue.
• Yes. Do you agree that there are $20$ possibilities to choose a pair of candies such that one of them is red and the other is blue? Btw, what do you mean with: "there are three candies in a basket". Maybe I misunderstand something there. Aren't there $14$ candies in total? – drhab Dec 10 '15 at 15:20
• Well then: $5\times 4+5\times5+4\times5=65$ possibilities. The first term corresponds with "red and blue" the second with "red and green" and the third with "blue and green". – drhab Dec 10 '15 at 15:30