M5.1.6 For the adult
Pascal's triangle and choosing
In how many ways can I choose 2 friends from 4?
What this chapter teaches
Pascal's triangle lists the coefficients of (a + b)ⁿ: row n gives the terms of (a + b)ⁿ, and each entry is the sum of the two above it. The same numbers count ways of choosing: nCr = n!/(r!(n − r)!) is the number of ways to choose r things from n when the order does not matter, with 0! = 1.
Three questions to ask
There is no one right wording. Listen for the idea.
- What are the numbers in row 4 of Pascal's triangle, and what do they give?
- In how many ways can you choose 2 friends from 5, and how can you tell without listing them?
- Why is 0! equal to 1?
After the chapter, the learner can
- Build Pascal's triangle and link it to (a + b)ⁿ
- Find nCr, the number of ways to choose r things from n
What they copy into their notebook
Pascal's triangle: each entry is the sum of the two above; row n gives (a + b)ⁿ. nCr = n!/(r!(n − r)!) counts choices; 0! = 1. nCr = nC(n − r).