Answer :
There are six people.
The first person can be born in any of the 12 months so probability is 12/12.
The second can be born in any of 11 so probability is 11/12.
The third one 10/12
Fourth , fifth and sixth person probability is 9/12,8/12 and 7/12 respectively.
Hence the probability is:
[tex]\frac{12}{12}\times\frac{11}{12}\times\frac{10}{12}\times\frac{9}{12}\times\frac{8}{12}\times\frac{7}{12}=\frac{385}{1728}\approx0.2228[/tex]Hence the probability that all six are born in different months of the year is 0.2228 or 22.28%.