Skip to lesson

Choose “Save as PDF” in the print dialog to keep a copy.

Cogito

Algebra 2 · Chapter 8 · Lesson 3

Practice Worksheet

Permutations and Combinations

Does the order change the answer?

12 problems · about 22 minutes · S-CP.B.9

NameDate

Figure — use these to answer the problems

Compare the counts: arranging always beats selecting, because order multiplies the possibilities.
Arrangements20
Selections10
Arrangements20
Selections10
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. How many ways can 3 books be arranged in a row?

    Answer

  2. Choosing a committee of 3 from 10 uses which count?

    • A combination, because order does not matter.
    • A permutation, because people are different.

  3. What is 5!?

    Answer

  4. What is 6C2?

    Answer

  5. What is 5P2?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. A menu has 3 starters and 4 mains. How many two-course meals?

    Answer

  2. What is 7C7?

    Answer

  3. How many 3-digit codes use digits 0 to 9 with repeats allowed?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Sort each situation by whether order matters.

    Write each item under the heading it belongs to: Awarding gold, silver and bronze · Choosing 3 players for a team · Setting a 4-digit passcode · Picking 2 toppings for a pizza

    Order matters

    Order does not matter

  2. What is 4C2?

    Answer

  3. The Shelf

    How many ways can 4 books be arranged in a row?

    Answer

  4. The Pizza

    How many ways can 2 toppings be chosen from 5, when order does not matter?

    Answer