MHB Probability of Student Seating Arrangement in Height Order

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In a class of 9 students with unique heights, the probability of them being seated in order from shortest to tallest is calculated by considering all possible arrangements. There are a total of 9! (factorial) possible seating arrangements, which equals 362,880. Only one specific arrangement corresponds to the order from shortest to tallest. Therefore, the probability of this specific arrangement occurring is 1 in 362,880, or 1/9!. This illustrates the rarity of achieving a perfect height order in random seating assignments.
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a class has 9 students who are to be assigned seating by lot. What is the probability that students will be arranged in order from shortest to tallest? (assume that no two stusents are the same height.)
 
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Same as picking 9 balls numbered 1 to 9 at random:
probability that order will be 1,2,3,4,5,6,7,8,9 ?
 

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