This morning my son said “I’m trying to work out how many ways there are putting up three fingers” (holding up one hand). I showed him if you put one finger down there are four choices which other finger to put down. Since there are five choices for which you put down first, that makes 5×4=20. Then I showed him that each pair could be put down two ways, so doing this meant we’d counted each pair twice, so the answer is 10. He wanted to know how this works for other numbers, which led us into a conversation involving factorials, which was pretty deep for an 8yo.
Then this afternoon he called me over and said he was trying to use this to work out how many teddy bears he could make. By pattern matching he’d found 8. I explained this was not the same problem because we aren’t choosing any three from six, but have to pick the right body parts. I showed him there are two sets of bears, one with each head. Then there are two sets, one with each body, and the same for legs. So there are 2×2×2=8 bears.
Add comment