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721All-Category Coverage Probability 16 independent tickets are each assigned uniformly to one of 3 categories. What is the probability that every category appears at least once?脑筋急转弯简单数值题未尝试免费5667Hat-Check Derangement CountSix guests check distinct hats. The attendant returns the hats in a random order. In how many of the possible return orderings does no guest receive their own hat?脑筋急转弯中等数值题未尝试免费5668Secret-Santa No Self-Draw ProbabilityFive people draw names uniformly at random from a hat containing all five of their own names, one draw each, forming a random permutation. What is the probability that nobody draws their own name?脑筋急转弯中等数值题未尝试免费5669Five Gifts Four Children SurjectionFive distinct gifts are distributed to 4 distinct children so that every child receives at least one gift. In how many ways can this be done?脑筋急转弯中等数值题未尝试免费5670Coprime-to-2357 Count up to 1000How many integers from 1 to 1000 are divisible by none of 2, 3, 5, or 7?脑筋急转弯中等数值题未尝试免费5671At-Least-One Fixed Point CountOf the 120 permutations of the labels 1,2,3,4,5 , how many fix at least one label in its original position?脑筋急转弯中等数值题未尝试免费5672Trilingual Survey None-CountIn a group of 100 people, 50 speak French, 40 speak German, 35 speak Spanish; 18 speak both French and German, 15 both French and Spanish, 12 both German and Spanish, and 6 speak all three. How many speak none of these three languages?脑筋急转弯简单数值题未尝试免费5673Totient of 60 by SieveHow many integers in the range 1 to 60 are relatively prime to 60 (share no common factor greater than 1 with 60)?脑筋急转弯中等数值题未尝试免费5674At-Least-One Couple ReunitedFour married women and their four husbands are randomly paired into 4 man-woman dance pairs (a uniform random perfect matching). What is the probability that at least one woman is paired with her own husband?脑筋急转弯中等数值题未尝试免费5675Seating with Forbidden Own-ChairFour people, each with an assigned chair, are reseated so that no person sits in their own assigned chair, and additionally person 1 must not sit in chair 2. How many seatings are valid?脑筋急转弯困难数值题未尝试免费5676Seven Tasks Four Machines All BusySeven distinct tasks are each assigned to one of 4 distinct machines. In how many assignments is every machine used at least once?脑筋急转弯中等数值题未尝试免费5951Three Prizes, Unequal OddsA claw machine yields prize 1 with probability 1/2, prize 2 with probability 1/3, and prize 3 with probability 1/6, independently each play. What is the expected number of plays to collect all three prizes?概率困难数值题未尝试面试订阅5953Collecting in PairsEach purchase gives you a PACK of 2 cards, where each of the 2 cards is independently and uniformly one of 4 types (the two cards in a pack may coincide). What is the expected number of PACKS you must buy to collect all 4 types?概率困难数值题未尝试面试订阅5954Just These TwoCoupons arrive uniformly and independently from 5 types. You only care about two SPECIFIC types, the gold and the silver coupon; the other three are worthless to you. What is the expected number of draws until you have collected BOTH the gold and the silver coupon?概率中等数值题未尝试免费5957The Busiest Bin3 balls are thrown independently and uniformly into 3 bins. Let M be the maximum load, i.e. the number of balls in the most-loaded bin. What is E[M]?概率中等数值题未尝试免费