Answer :
Final answer:
In a meeting with six people where everyone exchanges business cards with each other, a total of 15 business cards will be passed out.
Explanation:
To determine how many business cards will be passed out if you go to a meeting with five other people and everyone exchanges business cards, we need to calculate the number of handshakes that would occur in this scenario. This can be done using combinatorial mathematics and is analogous to calculating the number of handshakes in a group of people. In this case, there are a total of six people at the meeting. Each person needs to exchange cards with every other person exactly once. We use the formula for the number of combinations of n items taken k at a time, which is given by C(n, k) = n! / (k!(n-k)!). Since one person can exchange a card with another in only one way, we take k=2.
The formula simplifies to C(6, 2) = 6! / (2!(6-2)!) = (6 * 5) / (2 * 1) = 15 exchanges.
Therefore, 15 business cards will be passed out in total, making option (b) the correct answer.
