Answer:
[tex]\displaystyle \frac{54}{5405}[/tex].
Step-by-step explanation:
How many unique combinations are possible in total?
This question takes 5 objects randomly out of a bag of 50 objects. The order in which these objects come out doesn't matter. Therefore, the number of unique choices possible will the sames as the combination
[tex]\displaystyle \left(50\atop 5\right) = 2,118,760[/tex].
How many out of that 2,118,760 combinations will satisfy the request?
Number of ways to choose 2 red candies out a batch of 28:
[tex]\displaystyle \left( 28\atop 2\right) = 378[/tex].
Number of ways to choose 3 green candies out of a batch of 8:
[tex]\displaystyle \left(8\atop 3\right)=56[/tex].
However, choosing two red candies out of a batch of 28 red candies does not influence the number of ways of choosing three green candies out of a batch of 8 green candies. The number of ways of choosing 2 red candies and 3 green candies will be the product of the two numbers of ways of choosing
[tex]\displaystyle \left( 28\atop 2\right) \cdot \left(8\atop 3\right) = 378\times 56 = 21,168[/tex].
The probability that the 5 candies chosen out of the 50 contain 2 red and 3 green will be:
[tex]\displaystyle \frac{21,168}{2,118,760} = \frac{54}{5405}[/tex].
