Final answer:
To form a committee of 6 U.S. senators with 3 Democrats and 3 Republicans, we can use combination formula to find the number of ways. The formula is C(n, r) = n! / (r! * (n-r)!), where n is the total number of options and r is the number of options to be selected. After calculating the two combinations, we divide the result by the number of permutations to get the final answer.
Step-by-step explanation:
To form a committee of 6 U.S. senators with 3 Democrats and 3 Republicans, we must choose 3 Democrats from the 38 Democratic Senators and 3 Republicans from the 62 Republican Senators. The number of ways this can be done is given by the combination formula. The number of ways to choose 3 Democrats from 38 is denoted as C(38, 3) and the number of ways to choose 3 Republicans from 62 is denoted as C(62, 3). To calculate these values, we can use the formula C(n, r) = n! / (r! * (n-r)!), where n is the total number of options and r is the number of options to be selected.
Using the formula, C(38, 3) = 38! / (3! * (38-3)!) and C(62, 3) = 62! / (3! * (62-3)!). Evaluating these expressions, we find that C(38, 3) = 8,492 and C(62, 3) = 21,640. Therefore, the total number of ways to form the committee is C(38, 3) * C(62, 3) = 8,492 * 21,640 = 183,073,280. However, the order of selection does not matter, so we divide this value by the number of permutations of 3 Democrats and 3 Republicans, which is 3! * 3! = 6 * 6 = 36. Therefore, the final answer is 183,073,280 / 36 = 5,085,369, which is approximately 5,085,369 ways. Hence, the correct answer is not listed among the given options.