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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
(2nn)2n
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B
3n
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C
(2n)!2n
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D
(2nn)
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Solution

The correct option is B 3n
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 = 3n)

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