Permutations

bigbill

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Joined
Sep 18, 2012
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n athletes are @ a race track. with n lanes. How many ways are possible that no runnner is in the correct lane ? How many arrangements are possible where 1 or more athletes is in the correct lane ? The 2 answers are less than 7 digits long , the sums of their digits are the same.
How many athletes are present ? The sol'n is 7 !


I can solve a problem such as 4 letters, 4 envelopes, what is the chance of getting 1,2, 3,4 correctly in the right envelope ? This looks a bit more cryptic. Thanks and happy C'mas.
 
n athletes are @ a race track. with n lanes. How many ways are possible that no runnner is in the correct lane ? How many arrangements are possible where 1 or more athletes is in the correct lane ? The 2 answers are less than 7 digits long , the sums of their digits are the same.
How many athletes are present ? The sol'n is 7 !


I can solve a problem such as 4 letters, 4 envelopes, what is the chance of getting 1,2, 3,4 correctly in the right envelope ? This looks a bit more cryptic. Thanks and happy C'mas.

Both of these are examples of derangements. Scroll down to counting derangements.
 
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