A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

Explanation

To solve the problem of selecting 2 black balls and 3 red balls from a bag containing 5 black balls and 6 red balls, we can use the concept of combinations. Here’s a step-by-step breakdown of the solution:

### Step 1: Determine the number of ways to select black balls
We need to select 2 black balls from a total of 5 black balls. The number of ways to choose \( r \) items from \( n \) items is given by the combination formula:

\[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
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