Final answer:
To find the number of ways to select 6 shoes with exactly two pairs from 6 pairs of shoes, calculate the combinations of choosing two pairs and two individual shoes from the remaining pairs, then multiply these numbers together for the answer.The correct answer is B.
Step-by-step explanation:
To find the number of ways of selecting 6 shoes out of 6 pairs of shoes with exactly two pairs, we can break the problem down into steps. First, we must select two pairs. Since there are 6 pairs, there are 6 choose 2 ways to select the pairs. This calculation, also known as a combination, is equal to 6! / (2! * (6-2)!), which simplifies to 15.
Next, we need to select 2 individual shoes from the remaining 4 pairs, which can be done in 4 ways per pair (since we're avoiding making any new pairs). There are thus 4 * 4 ways to select two individual shoes from the remaining four pairs. Finally, we multiply the two numbers of outcomes to get the answer: 15 * 16 = 240.