The probability that in a family of five members, exactly two members have birthday on Sunday is

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 75 ways. Out of 5, three persons can have their birthdays on days other than Sundays in 63 ways and other 2 on Sundays. Hence, the required probability is= 5C2×6375=10×6375(Note that 2 persons can be selected out of 5 in 5C2 ways.)