به انگلیسی

Listing every combination

Mathematics · Algebra · ages 10-11

Name ______________________ Date ____________

Mia lists meals starter by starter: soup, then salad. For each starter she uses mains in this order: pasta, pie, fish. She has written soup with pasta, then soup with pie. What comes next?
- salad with pasta
- salad with fish
- soup with fish
- soup with pasta
Either flavour, lemon or berry, can go in any cone: plain, chocolate or wafer. Your list has lemon-plain, lemon-chocolate, lemon-wafer, berry-plain and berry-chocolate. Which pair is missing?
- berry with wafer
- lemon with wafer
- berry with plain
- lemon with plain
A cafe has 2 soups and 3 sandwiches. Each soup can go with any sandwich. How many different soup-sandwich pairs are possible?
- 6
- 5
- 7
When you choose one option from each of two groups and every pairing is allowed, the number of different pairs equals the two group sizes multiplied together.
Circle one: True False
Each top can pair with each skirt. Complete Priya's table so every pair appears once. Which pairs belong at X, Y and Z?
Top black skirt white skirt gold skirt
red X red-white red-gold
green green-black Y green-gold
blue blue-black blue-white Z
- red-black, green-white, blue-gold
- red-white, green-gold, blue-black
- red-gold, green-black, blue-white
Either bread, rye or oat, can have egg, jam or ham. List rye first, then oat. For each bread, list egg, jam, then ham. Which list follows this order and includes every pair?
- rye-egg, oat-egg, rye-jam, oat-jam, rye-ham, oat-ham
- rye-egg, rye-jam, rye-ham, oat-egg, oat-jam, oat-jam
- rye-ham, rye-jam, rye-egg, oat-ham, oat-jam, oat-egg
- rye-egg, rye-jam, rye-ham, oat-egg, oat-jam, oat-ham
A postcard shop offers 4 pictures, including forest, and 3 borders. Every picture can have any border. How many picture-border pairs use the forest picture?
Answer: ______________
A restaurant has starters soup, salad and bruschetta, and mains fish, chicken, pasta and beef. You will list starter by starter. What should you do first?
- Pair soup with fish, salad with chicken and bruschetta with pasta, then stop.
- Pair each starter with fish, then stop without trying the other three mains.
- Keep soup fixed and pair it with each main before changing starters.
A poster shop offers 2 shapes in each of 4 colours. It adds one new colour for both shapes. How many new shape-colour pairs does this add?
- 4
- 2
- 6
- 8
Ben can pair any of 3 starters with any of 3 mains. He lists 8 different valid pairs. What does this tell you?
- Three pairs are repeated: 3 + 3 = 6.
- One pair is missing: 3 x 3 = 9.
- The list has an extra pair: 3 + 3 = 6.

Top	black skirt	white skirt	gold skirt
red	X	red-white	red-gold
green	green-black	Y	green-gold
blue	blue-black	blue-white	Z

Answer key

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

Listing every combination W1-mt_gu0NPDvlhY-s1

soup with fish · List pasta, pie and fish for soup in the stated order before moving to salad.
berry with wafer · All three lemon pairs are listed. Berry is paired with plain and chocolate, but not wafer.
6 · Each of the 2 soups has 3 sandwich choices. That gives 2 x 3 = 6 pairs.
True · Each option in one group pairs with every option in the other. The pairs form equal rows, which multiplication counts.
red-black, green-white, blue-gold · Match each cell's row and column: X is red-black, Y is green-white and Z is blue-gold. These complete all nine different pairs.
rye-egg, rye-jam, rye-ham, oat-egg, oat-jam, oat-ham · Follow the required order: list egg, jam and ham for rye, then repeat that filling order for oat.
3 · The picture is fixed as forest. Only the border changes, giving 3 pairs.
Keep soup fixed and pair it with each main before changing starters. · Finish all four mains for soup before moving to salad. Repeat that process for each remaining starter.
2 · The new colour pairs with each of the 2 shapes, adding 2 pairs.
One pair is missing: 3 x 3 = 9. · A complete list has 3 x 3 = 9 pairs. Ben's 8 pairs are different and valid, so exactly one pair is missing.