Question

Find the probability that the birth days of six different persons will fall in exactly two calender months.

Answer 1

Here each person has 12 option So there are $6$ persons .total no. Of ways ${12}^6$

And out of $12$ months $2$ are randomly selected

So, no. of ways ${=}^{12}{C}_2$

Since, there are $2$ favorable choices available for every person have birthday in the same month and every one has $2^6$ favorable choices (months),

Hence, Total favorable choices $=2^6-2.$

Therefore required probability is ${=}^{12}{C}_2\frac{2^6-2}{{12}^6}$

$=\frac{4092}{{12}^6}$

$=\frac{341}{{12}^5}$