How is the total number of outcomes calculated?","back":"Multiply the options: $a \\times b$.","points":1},{"id":"629867f8-b040-413d-886c-4da14bb7b740","cardType":"cloze","front":"When choosing one item from each of several separate groups, you must [ ] the number of choices in each group.","back":"When choosing one item from each of several separate groups, you must multiply the number of choices in each group.","points":null},{"id":"5501d987-59fd-486d-9b0a-6a78197c7394","cardType":"basic","front":"A lunch offer has 2 wraps and 3 drinks. How many possible lunch combinations are there?","back":"$$2 \\times 3 = 6$.","points":1},{"id":"9444a642-bcee-443d-8870-6d59cd8ad06d","cardType":"basic","front":"Why is addition ($11 + 13$) incorrect for finding the number of boy-and-girl pairs from 11 boys and 13 girls?","back":"Addition gives the total number of students, not the number of possible combinations.","points":2},{"id":"f1860d99-b64b-4b85-bd39-573e6bce09b0","cardType":"cloze","front":"In counting problems, a calculated number of choices ($x$) must always be a [ ].","back":"In counting problems, a calculated number of choices ($x$) must always be a whole number.","points":null},{"id":"ad71cd34-b883-4147-82e4-d46b5ac73111","cardType":"basic","front":"A restaurant offers 4 starters, 6 mains, and 3 desserts. How many different three-course meals are possible?","back":"$$4 \\times 6 \\times 3 = 72$.","points":1},{"id":"dcc8abb7-6f2e-45ce-83ee-f05e55d1dd72","cardType":"basic","front":"What condition must be met to use the product rule directly for multiple stages?","back":"Every option at one stage must be allowed to go with every option at the next stage.","points":1},{"id":"5dd14437-5077-4b3c-afd3-65890e16ec2a","cardType":"basic","front":"A shop has 8 sandwiches and $x$ drinks. Sam claims there are 90 meal deal outcomes. Why is Sam wrong?","back":"

$90 \\div 8 = 11.25$
The number of drinks must be a whole number.

","points":2},{"id":"4003d549-23fc-4b55-88f2-99bc5874207c","cardType":"cloze","front":"Choosing \"without replacement\" means the number of options for the next stage [ ].","back":"Choosing \"without replacement\" means the number of options for the next stage decreases by 1.","points":null},{"id":"eaa74b2f-bdac-453e-9254-b3f62a78731a","cardType":"basic","front":"Two cards are dealt from a 52-card deck to two named people. How many outcomes are possible?","back":"$$52 \\times 51 = 2652$.","points":1},{"id":"129a4be2-a62f-4817-ad3a-2ec1f1fadb17","cardType":"basic","front":"Why is the second stage $51$ instead of $52$ when dealing two cards from a deck?","back":"One card has already been removed and cannot be chosen again.","points":2},{"id":"c19d0b24-ae36-4644-b539-a721a274f93f","cardType":"basic","front":"When calculating unordered pairs from $n$ items, what is the formula?","back":"$$$\\frac{n(n-1)}{2}$$","points":1},{"id":"4ca8946e-80e5-42d1-913f-dbd61fe86167","cardType":"cloze","front":"For handshakes or matches, we [ ] because each pair is counted twice (e.g., A-B and B-A).","back":"For handshakes or matches, we divide by 2 because each pair is counted twice (e.g., A-B and B-A).","points":null},{"id":"fb45b2ad-ff16-427b-ad02-e631a0fbd177","cardType":"basic","front":"28 students are in a class. Two are chosen for the same prize. How many possible pairs are there?","back":"$$$\\frac{28 \\times 27}{2} = 378$$","points":2},{"id":"3c65a4d6-c903-47fb-8d53-de4d54b9655d","cardType":"basic","front":"9 teams play each

The Product Rule for Counting Flashcards

The Product Rule for Counting Flashcards

The Product Rule for Counting Flashcards

The Product Rule for Counting Flashcards