MHB Johns Born Same Day: 24M Humans, 4 Letters

[mathworker]

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

 

[Albert1]

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

Spoiler

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