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).

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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