Probability of Student Seating Arrangement in Height Order

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SUMMARY

The probability of arranging 9 students in height order from shortest to tallest is calculated using combinatorial principles. Given that there are 9 unique heights, the total number of possible arrangements is 9! (factorial of 9), which equals 362,880. Only one of these arrangements corresponds to the students being seated in the correct order (1, 2, 3, 4, 5, 6, 7, 8, 9). Therefore, the probability is 1/362,880, or approximately 0.00000275573.

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rainbow1
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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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