Final answer:
The probability of grabbing 2 cherry and 1 orange candy from the bag is 3/11.
Step-by-step explanation:
To find the probability of grabbing 2 cherry and 1 orange candy, we need to calculate the favorable outcomes and divide it by the total outcomes.
The total number of candies in the bag is 6 (cherry) + 3 (orange) + 2 (lemon) = 11 candies.
The possible favorable outcomes are: choosing 2 cherry candies from the 6 available cherry candies and 1 orange candy from the 3 available orange candies. We can calculate this using the combination formula:
C(6, 2) * C(3, 1) = (6! / (2!(6-2)!) * (3! / (1!(3-1)!)) = 15 * 3 = 45
The total possible outcomes are choosing 3 candies from the 11 available candies:
C(11, 3) = 11! / (3!(11-3)!) = 165
Therefore, the probability of grabbing 2 cherry and 1 orange candy is 45/165, which simplifies to 3/11.