Predict number of Birthdays for 1000 person of same class in next 365 Days

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I want to know an approximate number of birthdays for a class where each month 1000 Persons are added up. Like 1st month its 1000, 2nd month its 2000, 3rd month it is 3000 And so on. Now lets say today is 1st Jan 2013, then upto 1st Jan 2014, How many birthdays we'll be having with our class in which every month 1000 persons are adding up so that upto 1st Jan 2014 We will be having 12000 Persons in our class. I want to calculate total number of birthdays from 1st jan 2013 to 1st Jan 2014.

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A person in the class in January has chance $1$ of having a birthday because he is in the class all year. That gets you $1000$ birthdays. A person who arrives in February has $\frac{365-31}{365}$ chance of having his birthday in class, so that group will on average get you $915$ birthdays. Keep going through the months and you will have your answer.

Slightly less accurately, because it ignores the differing numbers of days per month, you have on average $6500$ people in class, so you should have about $6500$ birthdays during the year.

I'm not sure this is at all what you are asking. Is it?