The probability that in a family of `5` members, exactly two members have birthday on sunday is:-

Options

A. `(12 xx 5^(3))/7^(5)`
B. `(10 xx 6^(2))/7^(5)`
C. `2/5`
D. `(10 xx 6^(3))/7^(5)`

Answer

D

Explanation

A person can have his/her birthday on any one of the seven days of the week. So 5 persons can have their birthdays in `7^(5)` ways. Out of 5, three persons can have their birthdays on days other than Sundays in `6^(3)` ways and other 2 on Sundays. Hence, the required probability is
`=(.^(5)C_(2) xx 6^(3))/(7^(5)) = (10 xx 6^(3))/(7^(5))`
(Note that 2 persons can be selected out of 5 in `.^(5)C_(2)` ways).