Answer:
The probability that they were born in different months is [tex]\frac{55}{144}[/tex]
Step-by-step explanation:
Total number of ways = 12
Number of ways of the first person = 12
So, probability for the first person is [tex]\frac{12}{12} =1[/tex]
Now, the number of ways for the second person = 11
So, the probability for him = [tex]\frac{11}{12}[/tex]
Similarly, the probabilities for third, fourth and fifth persons are:
[tex]\frac{10}{12},\frac{9}{12} and \frac{8}{12}[/tex]
Hence, the total number of ways = [tex]1(\frac{11}{12} )(\frac{10}{12} )(\frac{9}{12} )(\frac{8}{12} )[/tex]
[tex]=\frac{55}{144}[/tex]
