Final answer:
The number of ways to form a committee of 6 U.S. senators with 3 Democrats and 3 Republicans, given 62 Democratic and 38 Republican senators, is calculated using combinations and the final answer is 290,424,400 ways.
Step-by-step explanation:
To determine the number of ways a committee of 6 U.S. senators can be formed with 3 Democrats and 3 Republicans, we use combinations since the order in which we select the senators does not matter. Considering there are 62 Democratic senators and 38 Republican senators, we will calculate the number of combinations for both parties separately and then multiply them.
First, for the Democrats, we have C(62, 3), which is the number of combinations of 62 things taken 3 at a time. This can be calculated using the combination formula C(n, k) = n! / (k! * (n - k)!).
For the Republicans, we have C(38, 3), which follows the same combination principle.
Finally, we multiply these two values to get the total number of ways to form the committee: C(62, 3) * C(38, 3).
Combination Calculation:
Therefore, the total is 34,860 * 8,340, or 290,424,400 ways to form the committee with 3 Democrats and 3 Republicans.