(a) Show that in any groups of eight people, at least two were born on the same
day of the week.
(b) Show that in any group of 80 people, at least 12 were born on the same day
of the week.

Question

(a) Show that in any groups of eight people, at least two were born on the same
day of the week.
(b) Show that in any group of 80 people, at least 12 were born on the same day
of the week.

anonymous · Answer

well if there are 7 days in a week, and 8 people in a group, unless one person magically popped into existence...

anonymous · Answer

This is referred to as the pigeonhole principle. If you have 8 people, and only 7 days of the week on which they could be born, then one of those days has to have 2 people.