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Cogito

Probability and Statistics · Chapter 5 · Lesson 1

Practice Worksheet

Counting Principles

Count without listing.

12 problems · about 21 minutes · TEKS P.S.2.F, S-CP.B.9

NameDate

Figure — use these to answer the problems

Choosing 2 from 5: twenty arrangements but only ten selections, because order doubles the count.
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, since order does not matter.
    • A permutation.

  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. 3 starters and 4 mains. How many two-course meals?

    Answer

  2. How many 3-digit codes from digits 0 to 9, repeats allowed?

    Answer

  3. What is 7C7?

    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: Gold, silver and bronze medals · A 4-digit passcode · Choosing 3 players for a team · Picking 2 pizza toppings

    Order matters

    Order does not matter

  2. What is 4C2?

    Answer

  3. The Arrangement

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

    Answer

  4. The Selection

    How many ways to choose 2 toppings from 5?

    Answer