MHB Find the probability of choosing the same subset

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To find the probability that Ram and Shola choose the same subset of 16,384 items from a collection of 65,536 items, one must first calculate the total number of ways to choose 16,384 items from 65,536, which is given by the binomial coefficient C(65536, 16384). The probability that both randomly selected subsets are identical is then the ratio of the number of favorable outcomes (1, since there is only one way for them to pick the same subset) to the total outcomes (C(65536, 16384)). This results in a probability of 1 divided by C(65536, 16384). The discussion emphasizes the importance of understanding combinatorial calculations in determining probabilities in such scenarios.
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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.
 
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Hello and welcome to MHB, Diganta28! :D

Can you compute how many ways there are to choose 16384 items from 65536 items?
 
MarkFL said:
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
 
Diganta28 said:
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?
 

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