Cogito
Probability and Statistics · Chapter 5 · Lesson 1
Counting Principles
Count without listing.
12 problems · about 21 minutes · TEKS P.S.2.F, S-CP.B.9
What this lesson teaches
The student applies the fundamental counting principle, permutations and combinations.
- Multiply the options at each stage to count outcomes.
- Permutations count arrangements; combinations count selections.
- nCr is nPr with the r! orderings divided out.
Warm Up
Straightforward practice. Get the method working first.
5 problemsHow many ways can 3 books be arranged in a row?
Answer 6
Why 6.
Choosing a committee of 3 from 10 uses which count?
Answer A combination, since order does not matter.
Why A combination.
What is 5!?
Answer 120
Why 5 × 4 × 3 × 2 × 1.
What is 6C2?
Answer 15
Why 720 ÷ (2 × 24).
What is 5P2?
Answer 20
Why 5 × 4.
Build It Up
The same ideas with more to keep track of.
3 problems3 starters and 4 mains. How many two-course meals?
Answer 12
Why 3 × 4.
How many 3-digit codes from digits 0 to 9, repeats allowed?
Answer 1000
Why 10 × 10 × 10.
What is 7C7?
Answer 1
Why One way to take everything.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each situation by whether order matters.
Answer Order matters: Gold, silver and bronze medals, A 4-digit passcode · Order does not matter: Choosing 3 players for a team, Picking 2 pizza toppings
Why Ask whether swapping two chosen items changes the result.
What is 4C2?
Answer 6
Why 24 ÷ (2 × 2).
The Arrangement: How many ways can 4 books be arranged in a row?
Answer 24
Why 24.
The Selection: How many ways to choose 2 toppings from 5?
Answer 10
Why 10.