Inviting friends

Probability Level 4

A person has 10 friends.Over several days he invites some of them to a dinner party so that the company never repeats(he may invite nobody on one of the days).For how many days can he follow this rule?

Same company never repeats means same subset of people cannot repeat and also note that on one day only one subset of friends are invited.


The answer is 1024.

Ravi Dwivedi by Ravi Dwivedi , 24, India

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1 solution

Ravi Dwivedi
Jul 11, 2015

The answer is equivalent to number of subsets of a 10 10 element set including the empty set.

Answer= 2 10 = 1024 2^{10}=\boxed{1024}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

"company never repeats" needs to be defined better. Do you mean "not the exact same group of people" or "the same subset doesn't occur", or "on a given day X, no subset of those people have been exactly invited to dinner before".

This means the same subset doesn't occur again

Ravi Dwivedi - 5 years, 11 months ago

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