SOLUTION: minimum number of individual shoes to be picked up from a dark room(containing 10 pair of shoes). if we have to get at least one proper pair

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Question 570859: minimum number of individual shoes to be picked up from a dark room(containing 10 pair of shoes). if we have to get at least one proper pair
Found 2 solutions by Edwin McCravy, richard1234:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
11 individual shoes, for if you picked up only 10, you could possibly pick 10
left shoes and no right shoes, or vice-versa.  But if so, the 11th one has to
match one of the other 10.

For your information:

 If you pick          then the probability of
this many shoes,     getting one matched pair is

       1                        0
       2                     1/19 = .053
       3                     3/19 = .158 
       4                   99/323 = .307
       5                  155/323 = .480
       6                  211/323 = .653
       7                  259/323 = .802
       8                3815/4199 = .909  
       9                4071/4199 = .970 
      10              45933/46189 = .994 
      11                        1 

If you pick 6 shoes out of the 20 you are more likely than 
not to have picked a matching part.



Edwin

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
By Pigeonhole principle, if we have ten boxes corresponding to ten pairs of shoes and we have 11 shoes, two shoes must go into the same box (and hence, make a match).