How many combinations worksheet

Part A: Working out and filling in

1. 1. 6

   Think about just one flavour first: how many cones can it go in? Every flavour has the same number.

   Each flavour goes with 2 cones, so 3 flavours give 3 lots of 2: 3 × 2 = 6 different ice creams.

2. 2. 4

   Think about just one top first: how many skirts can it go with? Every top has the same number.

   Each top goes with 2 skirts, so 2 tops give 2 lots of 2: 2 × 2 = 4.

3. 3. 5

   Each of the 2 tops goes with the same skirts. What do you multiply 2 by to get 10?

   2 tops, each with the same skirts: 2 × □ = 10, so there are 5 skirts.

4. 4. 2, 4

   One top can go with every pair of trousers. Count the outfits for one top first, then think about 2 tops.

   One top goes with 2 pairs of trousers, and each of the 2 tops does: 2 × 2 = 4.

5. 5. 2, 10

   One top can go with every pair of trousers. Count the outfits for one top first, then think about 5 tops.

   One top goes with 2 pairs of trousers, and each of the 5 tops does: 5 × 2 = 10.

6. 6. 2

   Each of the 6 tops goes with the same skirts. What do you multiply 6 by to get 12?

   6 tops, each with the same skirts: 6 × □ = 12, so there are 2 skirts.

7. 7. 48

   First pair up just the bread and the drinks: how many ways are there?

   Each of those can then go with any of the 3 kinds of fruit.

   Bread with a drink makes 4 × 4 = 16; each goes with 3 fruits: 16 × 3 = 48.

8. 8. 36

   First pair up just the bread and the drinks: how many ways are there?

   Each of those can then go with any of the 3 kinds of fruit.

   Bread with a drink makes 3 × 4 = 12; each goes with 3 fruits: 12 × 3 = 36.

Part B: Choose, or true or false

1. 9. C. 12

   Take one kind of noodles: how many soups can it go with? Every kind has the same number.

   Each kind of noodles goes with 6 soups, so 2 kinds give 2 × 6 = 12.

2. 10. False

   Each top goes with 4 pairs of trousers. Work out how many outfits 6 tops make, then compare it with 28.

   Each top goes with 4 pairs, so 6 tops make 6 × 4 = 24.

3. 11. False

   Each top goes with 2 pairs of trousers. Work out how many outfits 3 tops make, then compare it with 5.

   Each top goes with 2 pairs, so 3 tops make 3 × 2 = 6.

4. 12. C. 12

   Take one kind of noodles: how many soups can it go with? Every kind has the same number.

   Each kind of noodles goes with 4 soups, so 3 kinds give 3 × 4 = 12.

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

1. 13. 3 outfits

   Which tops can the new pair go with? Count them.

   The new pair goes with every top, so 3 more: 6 outfits become 9.

2. 14. 8 ways

   Pick one flavour: how many ways can it come? Every flavour is the same.

   Each flavour comes 2 ways: 4 × 2 = 8.

3. 15. 4 breakfasts

   Each main goes with 2 drinks. With 2 mains, how many lots of 2 is that?

   Each main goes with 2 drinks: 2 × 2 = 4.

4. 16. 4 skirts

   Every top goes with every skirt, so each has the same number. What do you multiply 6 by to get 24?

   Each top goes with the same skirts: 6 × □ = 24, so □ = 4.

5. 17. 4 ways

   Pick one path to the park: how many ways are there on to the library? Every path to the park gives the same choice.

   Each path to the park joins any of the 2 paths on: 2 × 2 = 4.

6. 18. 25 breakfasts

   Each main goes with 5 drinks. With 5 mains, how many lots of 5 is that?

   Each main goes with 5 drinks: 5 × 5 = 25.