In a colony, there are 55 members. Every member posts a greeting card to all the members. How many greeting cards were posted by them?ans.

1. ### Break Down the Problem

To determine the total number of greeting cards posted by all members, we need to find out how many cards each member sends out and then multiply that by the total number of members.

2. ### Relevant Concepts

Each member sends a card to every other member. Therefore, each member will send out $n - 1$ cards, where $n$ is the total number of members.

3. ### Analysis and Detail

1. Identify the total number of members: $n = 55$
2. Each member sends a greeting card to $n - 1$ members: $\text{Cards per member} = n - 1 = 55 - 1 = 54$
3. To find the total number of cards, multiply the number of cards per member by the total number of members: $\text{Total Cards} = n \times (n - 1) = 55 \times 54$

4. ### Verify and Summarize

Calculating the total number of cards: $55 \times 54 = 2970$ Thus, the total number of greeting cards posted by all members is 2970.

Final Answer

The total number of greeting cards posted is 2970.