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Cogito

Integrated Math 2 · Chapter 8 · Lesson 3

Practice Worksheet

Counting and Fair Decisions

Counting outcomes, and using probability to decide.

12 problems · about 21 minutes · S-CP.B.9, S-MD.B.5

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 4 books be arranged in a row?

    Answer

  2. What makes a game fair?

    • The expected gain is zero once the cost is subtracted.
    • Every outcome is equally likely.

  3. What is 4 factorial?

    Answer

  4. What is 5C2?

    Answer

  5. What is 5P2?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. 3 shirts and 4 trousers. How many outfits?

    Answer

  2. Pays $20 with probability 0.25. Expected payout in dollars?

    Answer

  3. Expected payout $5, cost $5. Expected gain in dollars?

    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 first and second place · Setting a 4-digit passcode · Choosing 3 players for a team · Picking 2 pizza toppings

    Order matters

    Order does not matter

  2. What is 6C2?

    Answer

  3. The Committee

    How many ways to choose 3 people from 6, when order does not matter?

    Answer

  4. The Game

    Pays $10 with probability 0.1, costs $2. What is the expected gain, in dollars?

    Answerdollars