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![[Post New]](/templates/default/images/icon_minipost_new.gif) 23 Sep 2007 11:41:19 IST
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In a city , no person has identical set of teeth & there is no person without a btooth dont consider shape size , just consider pos. of teeth , find the max population of the city plzz solve this if u r a genius  |
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23 Sep 2007 13:23:02 IST
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No. of persons having 1 tooth = 32C1
No. of persons having 2 teeth = 32C2
No. of persons having 3 teeth = 32C3
Hence total no. of persons = 32C1 + 32C2 + 32C3 + ........ + 32C32
Now use : (1+x)n = nC0 + nC1x + nC2x2 + ........ + nCnxn
Put x=1 :
2n = nC0 + nC1 + nC2 + ........ + nCn
nC1 + nC2 + ........ + nCn = 2n - nC0 = 2n - 1
Hence, 32C1 + 32C2 + 32C3 + ........ + 32C32 = 232 - 1
Alternatively :
At place 1 a person can either have a tooth or not, no. of ways = 2
At place 2 a person can either have a tooth or not, no. of ways = 2
......
At place 32 a person can either have a tooth or not, no. of ways = 2
Total no. of ways = 232 (including the person having no tooth)
No. of persons with at least 1 tooth = 232 - 1
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Bipin Kumar Dubey
Chemical Dept.
IIT Kharagpur
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23 Sep 2007 13:51:19 IST
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Bipin sir have given the correct answer
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"Imagination is more important than knowledge."
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23 Sep 2007 20:34:56 IST
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dont get confused that from where that 32 came , its the max no. of teeth a person can have
cheers!!!!!!!!!!!!!!!!!
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