What is the probability that in a class of 18 people, there exists a group of 3 people born on the same day of the week?


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Question Number 199310 by necx122 last updated on 01/Nov/23

$W h a t i s t h e p r o b a b i l i t y t h a t i n a c l a s s$ $o f 18 p e o p l e, t h e r e e x i s t s a g r o u p o f 3$ $p e o p l e b o r n o n t h e s a m e d a y o f t h e$ $w e e k ?$
Commented by deleteduser1 last updated on 01/Nov/23

$1$
	Answered by deleteduser1 last updated on 01/Nov/23

	$T h e r e a r e o n l y 7 d a y s i n a w e e k, a n d t h e n u m b e r$ $o f p e o p l e h a s e x c e e d e d t w i c e t h a t a m o u n t,$ $t h e r e m u s t b e a g r o u p o f t h r e e p e o p l e w i t h t h e$ $s a m e d a y .$
	Commented by mr W last updated on 01/Nov/23

	$i n f o l l o w i n g e x a m p l e t h e r e i s n o$ $g r o u p o f t h r e e p e o p l e o n t h e s a m e d a y :$ $1 p e r s o n o n m o n d a y$ $1 p e r s o n o n t u e s d a y$ $2 p e o p l e o n w e d n e s d a y$ $2 p e o p l e o n t h u r s d a y$ $5 p e o p l e o n f r i d a y$ $7 p e o p l e o n s a t u r d a y$ $n o p e o p l e o n s u n d a y$
	Commented by deleteduser1 last updated on 01/Nov/23

	$W e c a n p i c k a g r o u p o f 3 f r o m t h e 5 o r 7 o n$ $F r i d a y o r S a t u r d a y r e s p e c t i v e l y$
	Commented by deleteduser1 last updated on 01/Nov/23

	$T h e q u e s t i o n {d i d n}^{'} t s t a t e ‘ ‘ o f^{'} {o n l y}^{'} 3 {p e o p l e}^{″}$ $o r a d a y w i t h 3 p e o p l e o n l y .$
	Commented by necx122 last updated on 01/Nov/23
	unfortunately, I dont know the exact answer as my son just brought it to me. It's quite tricky but I think I can understand from the analysis from the solvings. Thank you sirs.
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