data-cloze=\"1\" data-cloze-masked=\"true\">[ ] 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$$","points":2},{"id":"3c65a4d6-c903-47fb-8d53-de4d54b9655d","cardType":"basic","front":"9 teams play each other once in a league. How many games are played?","back":"$$$\\frac{9 \\times 8}{2} = 36$$","points":2},{"id":"241f91d4-0b52-439b-b07f-bc50eda84fd6","cardType":"cloze","front":"If two people are chosen for different roles, you

The Product Rule for Counting Flashcards

The Product Rule for Counting Flashcards

The Product Rule for Counting Flashcards

The Product Rule for Counting Flashcards