Question

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

Answer 1

The probability that they were born in different months is
`(55)/(144)`

Explanation:

Total number of ways = 12

Number of ways of the first person = 12

So, probability for the first person is
`(12)/(12) =1`

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

So, the probability for him =
`(11)/(12)`

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

`(10)/(12),(9)/(12) and (8)/(12)`

Hence, the total number of ways =
`1((11)/(12) )((10)/(12) )((9)/(12) )((8)/(12) )`

`=(55)/(144)`