M4.6.8 For the adult
Counting choices
Mei has 3 scarves and 2 hats. How many different outfits can she make with one scarf and one hat?
What this chapter teaches
The product rule: if one choice has a ways and another has b ways, doing both has a × b ways. When nothing can be used twice, each choice has one fewer option, so 4 different letters can be arranged in 4 × 3 × 2 × 1 = 24 ways. Counting gives the total for a probability.
Three questions to ask
There is no one right wording. Listen for the idea.
- Why do you multiply the numbers of scarves and hats, and not add them?
- Why does the second place in a row of four letters have only 3 choices?
- If a lock has 3 wheels of 10 digits, what is the chance of opening it with one random guess?
After the chapter, the learner can
- Count outcomes with the product rule
- Find how many ways there are to arrange 4 different letters
What they copy into their notebook
Product rule: a ways then b ways make a × b ways. Nothing used twice: the choices fall by one each time. 4 letters: 4 × 3 × 2 × 1 = 24.