a family has eight children If this family has exactly three

a family has eight children. If this family has exactly three boys, how many different birth and gender orders are possible?

Solution

there are all total 8 children out of which 3 are boys. so there are exactly 5 girls.

now excluding 29th february

the first child can born on any one of 365 days. the second child can also born any of the 365 days and so on.

so the total number of different birth orders is 365*365*365*365*365*365*365*365=(365)⁸    [answer]

and if same birthdays are not allowed then the first child can born on any of 365 days. 2nd child can born on any one of remaining 364 days. similarly the 3rd child has 363 days and so on

so total number of different birth orders is 365*364*363*362*361*360*359*358 [answer]

there are two genders- FEMALE and MALE

out of 8 children there are 5 FEMALES and 3 MALES.

which is equivalent to arranging 8 objects out of which 5 of a kind and 3 are of another kind.

so total number of gender orders= 8!/(5!*3!)=56 [answer]