If there are 7 people in the room, what
are the chances they were born on the
same day of the week? And explain why.

Suppose the seven people are Ann,
Betty, Charles, Don, Edith, Fran, and
George.

All 7 could have been born on the same
day of the week in 7 ways.

So the numerator of the probability is
7.

Ann could have been born on a day of
the week in 7 ways.

For each of those 7 ways, Betty could
have been born on a day of the week in
7 ways.

For each of those 7 ways, Charles could
have been born on a day of the week in
7 ways.

For each of those 7 ways, Don could
have been born on a day of the week in
7 ways.

For each of those 7 ways, Edith could
have been born on a day of the week in
7 ways.

For each of those 7 ways, Fran could
have been born on a day of the week in
7 ways.

For each of those 7 ways, George could
have been born on a day of the week in
7 ways.

So the denominator of the desired
probability is 7·7·7·7·7·7·7 or 77.

So the probability is  =  =  
or about 0.0000085.

Edwin