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+9 votes

$n$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is

  1. \(^{2n}\mathrm{C}_n\times 2^n\)
  2. \(3^n\)
  3. \(\frac{(2n)!}{2^n}\)
  4. \(^{2n}\mathrm{C}_n\)
asked in Combinatory by Veteran (66.1k points) 1148 2197 2522
retagged by | 755 views

2 Answers

+30 votes
Best answer

Possible outcome for a couple:

  1. only wife comes
  2. both come
  3. none come

Thus 3 possibilities for each couple, so 3 x 3 x 3 x ... n times = $3^n$

answered by Active (1.5k points) 2 18 30
selected by
It would be easy to understand If u give few examples along with the answer...

Thanks in advance

Here it is mentioned wife need not come with husband,

This may give 2 outcomes

wife comes with husband

wife comes with other person other than husband

possible outcomes are

wife comes with husband

wife comes with other person other than husband

husband with wife

and also none

Please clarify @Arjun Sir

@Jarvis You are inventing cases here , which are not there !
wife comes with other person other than husband = Wife not coming with husband !

We are given only 3 cases here !

  1. only wife comes
  2. both come
  3. none come

You might want to include few more cases , if you follow your logic !

Wife comes with Teddy bear :P and so on...

::D Teddy Bear
what is the meaning of none come

if wife is not present with husband  then husband cant come alone in party .. that is the third case in which nobody will come, beacuse their is a strict condition with husband.
consider a couple ,it can be $HW$,$WX$ or $XX$(none) .i.e a couple can be organized in 3 ways and we have $n$ couples .Use Multiplication  theorem $3*3*3*.....*3$ (n times)=$3^{n}$
0 votes

The correct answer is (B) 3n

answered by Boss (8.8k points) 3 8 12

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