Final answer:
A committee of two Democrats and one Republican can be formed in different ways by calculating the combinations of choosing two out of nine Democrats and one out of ten Republicans, then multiplying the two results.
Step-by-step explanation:
The question is asking how many different ways a committee of two Democrats and one Republican can be formed from a group of nine Democrats and ten Republicans.
To solve this, we use combinations, which are selections of items where the order does not matter. The formula for a combination is nCr = n! / (r!(n - r)!), where n is the total number of items to choose from, r is the number of items to be chosen, and ! represents the factorial of a number.
The number of ways to choose two Democrats out of nine is 9C2. The number of ways to choose one Republican out of ten is 10C1. The total number of ways to form the committee is the product of these two combinations, which gives us 9C2 × 10C1.