Lesson 16 of 48
Counting
Permutations, combinations, and why confusing them changes the answer.
Counting is the ground floor of probability: nearly every probability question is a counting question wearing a costume. Order matters or it does not, and getting that wrong is off by a factor of k-factorial.
Do this
Count one collection two genuinely different ways and get the same number. Then take a question where order matters and one where it does not, and compute both.
The question that unlocks the next lesson
You pick 3 people from 10 for a committee with no titles. Which count is right?
- A10 × 9 × 8, because you pick one at a time
- B10 × 9 × 8 ÷ 3!, because the order you picked them in does not matter
- C10³, because each slot has 10 choices
- D3! × 10, because the committee can be arranged 3! ways