Is Order Important in Permutations and Combinations for Probability?

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In permutations (nPr), the order of elements matters, while in combinations (nCr), it does not. The probability of an event is higher in combinations than in permutations because combinations account for the arrangement of elements without regard to order. When comparing probabilities, nCr yields a greater value than nPr when n and r are the same. The confusion arises from the relationship between permutations and combinations, where nPr equals nCr multiplied by r!. Understanding these distinctions clarifies the probability outcomes for both scenarios.
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[SOLVED] what's wrong with this

nPr= n!/(n-r)! and here in permutation order is important, and in combination
nCr= n!/( r!(n-r)! ) order is not important, so the propability of ana event will be more for combination from permutation, but permutation is combination times r!, so what is wrong with me and not with my question:smile:
 
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i don't know who told u that in permutation order is not important because i think it is important...that's the difference between permutation and combination.
 
sorry i was mistaken but now i corrected my question
 
the PROBABILITY will be more for combination
eg. nCr=7
and nPr= 60
so let's say the number 2 is in both then prob for nCr is 2/7
and for nPr it's 2/60
2/7 is greater than 2/60
am i making any sense?
i'm not sure if that's 100% right.
 
i didn't understand you, i mean if n and r are the same for combination and permutation, the result will be nCr > nPr, that is what I'm not understanding, but what is r and n in your post?
 
whatever r and n are...it doesn't matter because u want the probability, so if nPr>nCr, then the probaility of nCr is > prob of nPr.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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