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256 Questions
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need help
I have $5$ different mathematics textbooks and $4$ different psychology textbooks. In how many ways can I place the $9$ textbooks on a bookshelf, in a row, if all the psychology textbooks must be together, and all the mathematics textbooks must be toge
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13 déc. 2023
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50
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help counting
A speech class has five freshmen and four sophomores. (Everyone is distinguishable.) In how many ways can they stand in line, so that at least four of the freshmen are standing next to each other?
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13 déc. 2023
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58
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venn diagram
Dogs in the GoodDog Obedience School win a blue ribbon for learning how to sit, a green ribbon for learning how to roll over, and a white ribbon for learning how to stay. There are $100$ dogs in the school.
* $41$ have blue ribbons, $23$ have
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13 déc. 2023
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73
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help me
In the Olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are $3$ skaters, including $3$ Americans, in how many ways can the medals be awarded to three of the $3$ skaters if exactly
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13 déc. 2023
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76
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Counting
In the Olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are $3$ skaters, including $3$ Americans, in how many ways can the medals be awarded to three of the $3$ skaters?
<
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13 déc. 2023
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68
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help counting
North High School has a math club and a science club. There are a students in the math club and b students who are members of both clubs. The total number of students is c. Find an expression for the total number of students
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13 déc. 2023
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61
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+818
Counting
North High School has a math club and a science club. There are $a$ students in the math club and $b$ students who are members of both clubs. The total number of students is $c$. Find an expression for the total number of students
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13 déc. 2023
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32
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squares
Each square below is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the squares?
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13 déc. 2023
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61
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+818
need help
South High School offers only Chinese and Spanish. There are $5$ more students in Chinese than in Spanish, and every student takes at least one language. If there are a total of $12$ students in South High School, and $15$ students take only
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13 déc. 2023
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65
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+818
help me
At my office, $4$ people own cats, $2$ people own dogs, and $5$ people own both cats and dogs. How many people own a cat or a dog?
(Remember that in mathematics, the word "or" is used in the inclusive sense. So if you own
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13 déc. 2023
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Do not post AoPS homework.
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20 janv. 2025
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