Counting with the Product and Sum Rules · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Stages multiply, cases add

Mathematics · Discrete Mathematics · ages 18-19
Name ______________________   Date ____________

  1. A menu offers 2 soups and 3 salads as a starter. A diner picks exactly one starter. How many choices are there? Give a number.

    Answer: ______________

  2. Priya owns 3 shirts and 4 trousers. She wears one shirt with one pair of trousers. How many different outfits can she make?

    • 12
    • 7
    • 9
    • 16

  3. Priya owns 3 shirts and 4 trousers. She wears one shirt with one pair of trousers. How many different outfits can she make?

    • 12
    • 7
    • 9

  4. A choice made in stages, one pick after another, calls for multiplication.

    Circle one:   True   False

  5. Eight swimmers race for gold, silver, and bronze, with no ties. How many podium outcomes are possible?

    • 56
    • 21
    • 336

  6. Tom says a 2-person team can be chosen from 6 people in 6 times 5 = 30 ways. Is Tom right?

    Circle one:   True   False

  7. Five runners contest gold, silver, and bronze medals, with no ties. How many medal outcomes are possible?

    • 60
    • 15
    • 125
    • 10

  8. Five runners contest gold, silver, and bronze medals, with no ties. How many medal outcomes are possible?

    • 15
    • 60
    • 125

  9. A list names 10 French students and 8 German students, but 3 students take both languages. How many distinct students are on the list?

    • 18
    • 15
    • 13

  10. Ana counts 3 shirts with 4 trousers as 3 plus 4, or 7 outfits. What is her mistake?

    • The total is 7 because stages add
    • The total is 11 after removing overlap
    • She added stages that multiply; the total is 12
LightMySky · lightmysky.comW1-mt_3NZC5F7RKP-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Stages multiply, cases add W1-mt_3NZC5F7RKP-s1

  1. 5 · Soup or salad is a choice of disjoint cases: 2 plus 3 = 5.
  2. 12 · Each of the 3 shirts pairs with each of the 4 trousers: 3 times 4 = 12.
  3. 12 · Each shirt pairs with each trousers: 3 times 4 is 12.
  4. True · Stages in sequence multiply, while cases among groups add.
  5. 336 · Gold has 8 options, silver 7, bronze 6: 8 times 7 times 6 is 336.
  6. False · Tom is wrong. 6 times 5 counts ordered pairs, but team order does not matter, so each team is counted twice and the answer is 15.
  7. 60 · Gold has 5 options, silver then has 4, bronze then 3: 5 times 4 times 3 = 60.
  8. 60 · Gold has 5 options, silver then 4, bronze then 3: 5 times 4 times 3 is 60.
  9. 15 · The 3 students in both lists were counted twice: 10 plus 8 minus 3 is 15.
  10. She added stages that multiply; the total is 12 · Shirt then trousers is a sequence, so the counts multiply to 12.
Worksheet · LightMySky