Johns Born Same Day: 24M Humans, 4 Letters

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mathworker
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Prove that least two humans named John should have born on same day(means with same D.O.B) if world has only 24 million humans and their alphabet chart contain just 4 letter 'J','H','O' and 'N' and there can't be more than one million humans of same name and world started just 2739 years ago.

source:Pigeon hole principle
 

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mathworker said:
Prove that least two humans named John should have born on same day(means with same D.O.B) if world has only 24 million humans and their alphabet chart contain just 4 letter 'J','H','O' and 'N' and there can't be more than one million humans of same name and world started just 2739 years ago.

source:Pigeon hole principle
let x=numbers of humans with the same name

x=$\dfrac {24\times 1000000}{4!}=1000000$

$\dfrac {1000000}{365}=2739.726027397$(suppose world started just 2739 years ago)

$\dfrac {2739.726027397}{2739}>1 $

$\therefore$ at least two humans named John should have born on same day
 
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