BdMO Online Forum

Posted: **Thu Mar 18, 2021 10:10 pm**

এবারের IMO তে সিদ্ধান্ত নেওয়া হল প্রতিটি দলে 10 জন করে সদস্য থাকবে। দলের অন্তত দুইজনের জন্মদিন একই বার/সপ্তাহের একই দিনে হবার সম্ভাবনা কত ??
In this years IMO a decision has been taken that each team will be consist of 10 members. What is the probability that at least two people will have a birthday on the same day of the week?

Posted: **Sat Mar 20, 2021 8:03 am**

By using PHP we get that at least 2 people will have birthday on the same day of the week. So probability=1

Posted: **Sat Mar 20, 2021 1:23 pm**

Can you explain ??
What is PHP ??

Posted: **Sun Mar 21, 2021 8:54 pm**

203166 wrote: ↑
Sat Mar 20, 2021 1:23 pm
Can you explain ??
What is PHP ??

PHP stands for Pegion-hole Principle. It just says that if you have more pigeons than pigeon holes and you want to stack the pigeons in the holes then one pigeon hole must contain more than 1 pegion.
In the problem, we can compare the players as pigeons and the days of the week as pigeon holes and then apply PHP

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