Question

Given 30 people,probability that among 12 months there are 6 containing 2 bitrhdays and 6 containing 3 birthday each

Answer 1

Answer:

Step-by-step explanation:

Line up the students in order of Student Number. For each of them, write down the birth month. Under our assumption, there are 1230 equally likely sequences.

Now we count the sequences that satisfy our condition. There are (126) ways to choose the months that have 2 birthdays.

For definiteness concentrate on the choice January through June. There are (3012) ways to choose the students who will have birthdays in this set of months, and there are then 12!26 ways to assign them to the individual months. And for each of these ways, there are 18!(3!)6 ways to choose the students who will have birthdays in the various remaining months.

It remains to put the pieces together.

Remark: Your analysis is along the right lines. One thing that is missing is the term (126) representing the choice of months that will have two birthdays. But apart from that slip your analysis is more efficient than mine.

Hope it helps you...