recategorized by
689 views
2 votes
2 votes

There are five buckets, each of which can be open or closed. An arrangement is a specification of which buckets are open and which bucket are closed. Every person likes some of the arrangements and dislikes the rest. You host a party, and amazingly, no two people on the guest list have the same likes and dislikes. What is the maximum number of guests possible?

  1. $5^{2}$
  2. $\binom{5}{2}$
  3. $2^{5}$
  4. $2^{2^{5}}$
recategorized by

2 Answers

6 votes
6 votes
There are $5$ buckets and each of them can be opened and Closed i.e. $2$ options for each bucket.

 

so number of arrangements of buckets $= 2*2*2*2*2 = 2^5 = 32$

 

Now for of these $32$ arrangement a person can either select the arrangement or reject the arrangement i.e. $2$ options for each arrangement.

 

So the number of ways in which every person can select a set of arrangements such that set of his arrangements selected are different from other person's selection

$ = 2*2*2*2....32 \ times $

$= 2^{32} $

$= 2 ^{2^5} $

 

Hence Option $D.$ is the correct answer.
Answer:

Related questions

1 votes
1 votes
1 answer
3
Arjun asked Sep 23, 2019
425 views
Consider all possible words obtained by arranging all the letters of the word $\textbf{AGAIN}$. These words are now arranged in the alphabetical order, as in a dictionar...
1 votes
1 votes
2 answers
4
Arjun asked Sep 23, 2019
631 views
Five letters $A, B, C, D$ and $E$ are arranged so that $A$ and $C$ are always adjacent to each other and $B$ and $E$ are never adjacent to each other. The total number of...