1. Students should choose nine answers from the grid and place them
Choices – Bingo Method
Students should choose nine answers from the grid and place them
randomly into a 3x3 square in their book.
You may want to pause your display and choose questions
according to difficulty during the game.
Depending on time, students could win with
a line, an X, or a ‘full house’ (all).

2. Printing To print handouts from slides -
Select the slide from the left. Then click:
File > Print > ‘Print Current Slide’
To print multiple slides -
Click on a section title to highlight all those slides,
or press ‘Ctrl’ at the same time as selecting slides to
highlight more than one. Then click:
File > Print > ‘Print Selection’
To print double-sided handouts -
Highlight both slides before using ‘Print Selection’.
Choose ‘Print on Both Sides’ and ‘Flip on Short Edge’.

3. BINGO! 45 54 23 82 37 12 76 25 91
Product Rule
For Counting

4. Choose your numbers…
126
720
10000 48 15 56
507 35 36
190
252
2197 20
1000
120 84
Draw a 3x3 grid in your book.

5. How many ways can these letters be ordered?
Does
order
matter?
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠=𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔
=𝑁𝑜. 𝑜𝑓 1𝑠𝑡 𝐶ℎ𝑜𝑖𝑐𝑒𝑠×𝑁𝑜. 𝑜𝑓 2𝑛𝑑 𝐶ℎ𝑜𝑖𝑐𝑒𝑠× ..
=5×4×3×2×1
=120

6. Choose one from each list
A restaurant has this menu.
£3.95 Lunch!
Choose one from each list
Sandwich
Side
Drink
Cheese
Beans
Tea
Ham
Coleslaw
Coffee
Egg
Corn
Water
Tuna
Juice
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠=𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔
=𝑁𝑜. 𝑜𝑓 1𝑠𝑡 𝐶ℎ𝑜𝑖𝑐𝑒𝑠×𝑁𝑜. 𝑜𝑓 2𝑛𝑑 𝐶ℎ𝑜𝑖𝑐𝑒𝑠× ..
=4×3×4
=48

7. How many different 3-digit combinations can be made on this keypad?1 2 3 4 5 6 7 8 9
Does
order
matter?
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠=𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔
=𝑁𝑜. 𝑜𝑓 1𝑠𝑡 𝐶ℎ𝑜𝑖𝑐𝑒𝑠×𝑁𝑜. 𝑜𝑓 2𝑛𝑑 𝐶ℎ𝑜𝑖𝑐𝑒𝑠× ..
=10×10×10
=1000

8. How many ways can three letters be chosen?D B C A F G
Does
order
matter?
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠= 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑑𝑢𝑝𝑙𝑖𝑐𝑎𝑡𝑒𝑠
= 7×6×5 3×2×1
=35

9. How many different 3-digit combinations that must start with a letter
can be made on this keypad? 3 2 1 5 4 8 7 6 9
Does
order
matter? C B A
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠=𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔
=𝑁𝑜. 𝑜𝑓 1𝑠𝑡 𝐶ℎ𝑜𝑖𝑐𝑒𝑠×𝑁𝑜. 𝑜𝑓 2𝑛𝑑 𝐶ℎ𝑜𝑖𝑐𝑒𝑠× ..
=3×13×13
=507

10. A basketball team of 5 players is chosen from 10 players on the squad.
How many ways can a team be chosen?
Does
order
matter?
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠= 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑑𝑢𝑝𝑙𝑖𝑐𝑎𝑡𝑒𝑠
= 10×9×8×7×6 5×4×3×2×1
=252

11. A pizza restaurant has a choice of 6 toppings. You can choose
4 different toppings for a pizza.
How many different pizzas are possible?
Does
order
matter?
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠= 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑑𝑢𝑝𝑙𝑖𝑐𝑎𝑡𝑒𝑠
= 6×5×4×3 4×3×2×1
=15

12. How many ways can these numbers be ordered?4 6 7 8 2 9
Does
order
matter?
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠=𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔
=𝑁𝑜. 𝑜𝑓 1𝑠𝑡 𝐶ℎ𝑜𝑖𝑐𝑒𝑠×𝑁𝑜. 𝑜𝑓 2𝑛𝑑 𝐶ℎ𝑜𝑖𝑐𝑒𝑠× ..
=6×5×4×3×2×1
=720

13. Choose one from each list
A restaurant has this menu.
£3.95 Lunch!
Choose one from each list
Sandwich
Side
Drink
Cheese
Beans
Tea
Ham
Coleslaw
Coffee
Tuna
Corn
Water
Juice
Does
order
matter?
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠=𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔
=𝑁𝑜. 𝑜𝑓 1𝑠𝑡 𝐶ℎ𝑜𝑖𝑐𝑒𝑠×𝑁𝑜. 𝑜𝑓 2𝑛𝑑 𝐶ℎ𝑜𝑖𝑐𝑒𝑠× ..
=3×3×4
=36

14. How many different 4-digit combinations can be made on this keypad?1 2 3 4 5 6 7 8 9
Does
order
matter?
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠=𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔
=𝑁𝑜. 𝑜𝑓 1𝑠𝑡 𝐶ℎ𝑜𝑖𝑐𝑒𝑠×𝑁𝑜. 𝑜𝑓 2𝑛𝑑 𝐶ℎ𝑜𝑖𝑐𝑒𝑠× ..
=10×10×10×10
=10000

15. How many ways can four letters be chosen?D B C A F G H I
Does
order
matter?
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠= 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑑𝑢𝑝𝑙𝑖𝑐𝑎𝑡𝑒𝑠
= 9×8×7×6 4×3×2×1
=126

16. A sandwich shop has this menu.
Choose 3 ingredients!
Cheese
Ham
Egg
Bacon
Lettuce
Turkey
Does
order
matter?
How many different types of sandwich are available?
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠= 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑑𝑢𝑝𝑙𝑖𝑐𝑎𝑡𝑒𝑠
= 6×5×4 3×2×1
=20

17. How many different 3-digit combinations can be made on this keypad?2 1 5 4 8 7 6 9
Does
order
matter? C B A
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠=𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔
=𝑁𝑜. 𝑜𝑓 1𝑠𝑡 𝐶ℎ𝑜𝑖𝑐𝑒𝑠×𝑁𝑜. 𝑜𝑓 2𝑛𝑑 𝐶ℎ𝑜𝑖𝑐𝑒𝑠× ..
=13×13×13
=2197

18. A sandwich shop has this menu.
Choose 3 ingredients!
Cheese
Ham
Egg
Bacon
Lettuce
Turkey
Cucumber
Beef
Does
order
matter?
How many different types of sandwich are available?
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠= 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑑𝑢𝑝𝑙𝑖𝑐𝑎𝑡𝑒𝑠
= 8×7×6 3×2×1
=56

19. 20 teams play each other once. How many games will be played?
In a football league
20 teams play each other once.
How many games will be played?
Does
order
matter?
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠= 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑑𝑢𝑝𝑙𝑖𝑐𝑎𝑡𝑒𝑠
= 20×19 2×1
=190

20. A pizza restaurant has a choice of 9 toppings. You can choose
3 different toppings for a pizza.
How many different pizzas are possible?
Does
order
matter?
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑈𝑛𝑖𝑞𝑢𝑒 𝐶ℎ𝑜𝑖𝑐𝑒𝑠= 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑅𝑢𝑙𝑒 𝐹𝑜𝑟 𝐶𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑑𝑢𝑝𝑙𝑖𝑐𝑎𝑡𝑒𝑠
= 9×8×7 3×2×1
=84

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