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What is the remainder when $$3^{283}$$ is divided by 5?
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At a certain university, 60% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?
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In a box, the probability that the red ball is selected is 5/8. Mark randomly selects balls twice from the box without replacement. If he didn`t get a red ball in the first attempt, then the probability that he gets a red ball in the second attempt is 2/3. What is the probability that Mark get at least one red ball?
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2< x< 5, 1/10< y< 1/5
Quantity A: x+y
Quantity B: (1/x) + (1/y)
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A list contains 20 songs, Mike and Scott got the identical list. Mike marked 15 favorite songs, and Scott marked 12 songs. Which of the following cannot be the number of songs they both marked as favorite?
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A teacher has 3 courses in total. The average number of students who sign up for these courses is 32. Among these students, 5 students sign up for 2 courses, 3 students sign up for all the 3 courses. How many different students sign up for these courses in total?
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In how many ways can letter a b and c be assigned into a 3*3 nine palace such that no letter is used more than once in each line and each row?
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If 7 white cubes and 20 red cubes, all of equal size, are fastened together to form one large cube as shown above, what is the greatest fractional part of the surface area of the large cube that could be red?
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40 DVDs (17 are about psychology, 14 are about biology, and 9 are about history) need to be arranged in a bookshelf such that the 9 history-related DVDs are, on the whole, arranged in chronological order. How many ways can these DVDs be arranged?
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If the probability for each cannon shoots the target is 0.6, then at least how many cannons shoot together can you ensure the overall probability of shooting the target reach 0.99?
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