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?
BDMO-2020 Regional Prb
- Mehrab4226
- Posts:230
- Joined:Sat Jan 11, 2020 1:38 pm
- Location:Dhaka, Bangladesh
Re: BDMO-2020 Regional Prb
By using PHP we get that at least 2 people will have birthday on the same day of the week. So probability=1
The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
-Henri Poincaré
-Henri Poincaré
Re: BDMO-2020 Regional Prb
Can you explain ??
What is PHP ??
What is PHP ??
- Mehrab4226
- Posts:230
- Joined:Sat Jan 11, 2020 1:38 pm
- Location:Dhaka, Bangladesh
Re: BDMO-2020 Regional Prb
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
The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
-Henri Poincaré
-Henri Poincaré