Bob Lochel’s random “Matt” problem

Saw a fun tweet from Bob Lochel last week:

For today’s Family Math problem I thought I’d talk through the math behind this situation with my younger son.

First I showed him what had happened and asked for a few ideas about how to approach finding the probability that all of the Matt’s would end up in group d. It has been a while since we’ve done a probability and counting project, but the ideas came back to him as we talked:

Next we talked about how to calculation the number of different ways to put the students into the the groups of 5 and 4. Then I asked my son to estimate what the number was without calculating. His estimate was off and we returned to why in part 4 of the project:

Now we calculated the number of ways to arrange the students with all 3 Matt’s landing in group D. Once we had that number we found the probability of the outcome that happened. I also asked my son if he thought the outcome happened by random chance, or was Bob possibly playing a little joke:

Finally, we revisited the calculation from part 2 of the project. It turned out that his estimate actually was nearly right – investigating where it went wrong was a good use of time. Once we had the exact value by hand, we also computed the exact probability for the original problem by hand.

Thanks to Bob Lochel for sharing this fun outcome. If you’d like to see a similar probability / counting problem check out our exploration of the “Snapchat problem” from a few years ago:

Exploring the “Shapchat Problem” with my kids