n couples are invited to a party with the condition that every husband should…
2003
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.
A
- B.
B
- C.
C
- D.
D
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Correct answer: B
For each of the n couples, there are three possibilities: (1) neither attends, (2) only the wife attends, or (3) both attend. Since a husband must be accompanied by his wife if he attends, the husband cannot come alone. This gives 3 options per couple, so the total number of gatherings is 3^n.