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-

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 AST last updated on 01/Nov/23

1

Answered by AST last updated on 01/Nov/23

There are only 7 days in a week,and the number of people has exceeded twice that amount, there must be a group of three people with the same day.

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

in following example there is no group of three people on the same day: 1 person on monday 1 person on tuesday 2 people on wednesday 2 people on thursday 5 people on friday 7 people on saturday no people on sunday

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 AST last updated on 01/Nov/23

We can pick a group of 3 from the 5 or 7 on Friday or Saturday respectively

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 AST last updated on 01/Nov/23

The question didn′t state “of ′only′ 3 people” or a day with 3 people only.

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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