Question

In a group of 5 people, what is the probability they were all born in different months

Answer 1

Answer:

The probability that they were born in different months is $\frac{55}{144}$

Step-by-step explanation:

Total number of ways = 12

Number of ways of the first person = 12

So, probability for the first person is $\frac{12}{12} =1$

Now, the number of ways for the second person = 11

So, the probability for him = $\frac{11}{12}$

Similarly, the probabilities for third, fourth and fifth persons are:

$\frac{10}{12},\frac{9}{12} and \frac{8}{12}$

Hence, the total number of ways = $1(\frac{11}{12} )(\frac{10}{12} )(\frac{9}{12} )(\frac{8}{12} )$

$=\frac{55}{144}$