Find the probability of choosing the same subset

[Diganta281]

There is a collection of 65536 different items. Out of these items ,
Ram chooses 16384 items.Shola also wants to choose 16384 items out of
this collection of 65536 different items. Find the probability that
the collection of items which Ram has choosen will be same as the
collection of items which Shola will choose.

 

[MarkFL]

Hello and welcome to MHB, Diganta28! :D

Can you compute how many ways there are to choose 16384 items from 65536 items?

 

[Diganta281]

Hello and welcome to MHB, Diganta28! :D

Can you compute how many ways there are to choose 16384 items from 65536 items?

Ram randomly picks and Shola also picks randomly

 

[MarkFL]

Ram randomly picks and Shola also picks randomly

Yes, but how many ways are there to randomly pick 16384 items from a set of 65536 items, and how many ways can they both pick the same subset?

 

[CellCoree]

The probability of choosing the same subset of 16384 items out of a collection of 65536 different items is 1/65536, or approximately 0.000015%. This is because there is only one possible combination that both Ram and Shola could choose, out of the 65536 possible combinations. This is assuming that both Ram and Shola are choosing their items randomly and independently of each other.