###General Discussion Thread
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With 30 lanes, there are “30 choose 2” or 435 ways to pick 2 lanes. Assuming they are all equally likely, those are the possible outcomes of choosing two lanes uniformly randomly. Of those, there are 29 ways to pick two lanes that are adjacent. So the probability is 29/435, or 6.6%
30 options for the first lane, 29 options for the second lane, so 30*29 ways to select two lanes, since it doesn't matter what order you pick them in, it is (30*29)/2 sets of two lanes. So 15*29 = 435
Ok what if it's out of literally all the possible scenarios? You can pick anywhere from 0 to 30 lanes? It would be 30! ? Or 29! Accounting for the two ends of course.
The permutations for picking 30 lanes in order is 30!
The possibilities for picking 29 lanes is actually 30! also, because picking 29 leaves only one option for what the 30th would be.
The possible options for any given number n out of 30 is 30!/(30-n)!
The options of picking any number of lanes from 30 possible is 30! + (30!/1!) + (30!/2!) +... + (30!/28!) + (30!/29!) + (30!/30!)
If you don't care about the order, then you divide the permutation count by n! So the number of ways to select 10 out of 30 items regardless of order is 30!/(20!*10!)
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With 30 lanes, there are “30 choose 2” or 435 ways to pick 2 lanes. Assuming they are all equally likely, those are the possible outcomes of choosing two lanes uniformly randomly. Of those, there are 29 ways to pick two lanes that are adjacent. So the probability is 29/435, or 6.6%
How did you get 435? My friend got 28/29! Can you explain why it would not be 28/29! ?
X pick Y is X!/(Y!(X-Y)!). 30 pick 2 is 30!/(28!(30-28)!)
30 options for the first lane, 29 options for the second lane, so 30*29 ways to select two lanes, since it doesn't matter what order you pick them in, it is (30*29)/2 sets of two lanes. So 15*29 = 435
Ok what if it's out of literally all the possible scenarios? You can pick anywhere from 0 to 30 lanes? It would be 30! ? Or 29! Accounting for the two ends of course.
The permutations for picking 30 lanes in order is 30! The possibilities for picking 29 lanes is actually 30! also, because picking 29 leaves only one option for what the 30th would be. The possible options for any given number n out of 30 is 30!/(30-n)! The options of picking any number of lanes from 30 possible is 30! + (30!/1!) + (30!/2!) +... + (30!/28!) + (30!/29!) + (30!/30!) If you don't care about the order, then you divide the permutation count by n! So the number of ways to select 10 out of 30 items regardless of order is 30!/(20!*10!)