An urn contains 4 blue balls and 6 orange balls. in how many ways can we select 2 blue balls and 5 orange balls from the urn? a) 24 b) 38 c) 36 d) 732 e) 8637 f) none of the above.

b) 36

Step-by-step explanation:

We can use combinations to solve this problem.

The binomial coefficient counts the number of ways of choose k elements from a set of n elements.

The product rule from combinatorics says that if there are N ways of doing something and M ways of doing another thing, the number of ways of doing both things is equal to NM.

First, we choose the blue balls. The urn contains 4 blue balls and we select 2 so there are ways of doing this. Similarly, we choose the 5 orange balls from the set of 6 in the urn, which can be done in ways. By the product rule, there are MN=6(6)=36 ways of selecting all the balls.

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