I am not a mathematician but I'm giving a lecture on the scope of a number of people in a given group to interact.
- There are 40 people in an affinity group
- Each person has 10 unique items of knowledge relevant to a given subject matter
- they meet to converse.
- a conversation can be defined as sharing any one of the 10 items that each person has with any other two, three or four people in the whole group.
Is there a simple formula for figuring out the total number of permutations and combinations of different discussions that could be had. If there is not could someone give me an estimate or calculation of the number.
For three people meeting, you have $40 \choose 3$ ways to pick the group of three. Then if only one of them shares exactly one fact, you have $3$ ways to choose the sharer and $10$ ways for the sharer to choose the fact, for a total ${40 \choose 3}\cdot 3 \cdot 10=296,400$ conversations. For sharing with $3$ or $4$, you can just change the $3$'s to $4$ or $5$
If each person in a three way conversation shares one fact, you have $40 \choose 3$ ways to choose the group and each one has $10$ choices of facts, giving ${40 \choose 3}10^3=9,880,000$ three way conversations.