Question

There are twelve friends. On the eve of Diwali, they exchanged greeting cards among themselves. How many cards did they exchange altogether?

• A. 132
• B. 66
• C. 264
• D. None of the above

Hint:

Remember: Handshakes are shared (divide by 2), but Gifts/Cards are one-way (do not divide by 2). The formula is just \( n(n-1) \).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Unlike a handshake (where one action involves two people), exchanging cards means if Friend A gives a card to Friend B, Friend B also gives a card to Friend A. This is a problem of permutations or simple multiplication.

Step 2: Key Formula or Approach:
Total exchanges = $n \times (n - 1)$

Step 3: Detailed Explanation:
1. Total number of friends $n = 12$. 2. Each friend will give a card to every other friend except themselves. 3. So, each person gives $(12 - 1) = 11$ cards. 4. Total cards = $12 \text{ friends} \times 11 \text{ cards per friend} = 132$.

Step 4: Final Answer:
They exchanged 132 cards altogether.