Question

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

• A. $(\frac{2n}{n})\ast 2^n$
• B. $3^n$
• C. $\frac{\left(2n\right)!}{2^n}$
• D. $(\frac{2n}{n})$

Answer 1

The correct option is B $3^n$

For each of the n couples invited to the party one of three thing is possible:

1. Both husband and wife attend the party.
2. Wife only attends the party
3.Neither husband nor wife attends the party.

Since there are n such couples, total number of possibilities = $3^n$)