2 men and 1 woman board a bus in which 5 seats are vacant. One of these five seats is reserved for ladies. A woman may or may not sit on the seat reserved for ladies but a man cannot sit on the seat reserved for ladies. In how many different ways can the five seats be occupied by these three passengers?
- A15
- B36Correct
- C48
- D60
Explanation
To solve this, we consider two scenarios based on where the woman sits.
Scenario 1: The woman sits on the reserved seat. There is only 1 way for the woman to choose this seat. After she sits, there are 4 vacant seats remaining for the 2 men. The first man can choose any of the 4 seats, and the second man can choose any of the remaining 3 seats. Calculation: 1 multiplied by 4 multiplied by 3 equals 12 ways.
Scenario 2: The woman sits on one of the 4 unreserved seats. There are 4 ways for the woman to choose a seat. After she sits, there are 4 vacant seats left, but 1 of them is the reserved seat which the men cannot use. Therefore, the 2 men must choose from the 3 remaining unreserved seats. The first man has 3 choices, and the second man has 2 choices. Calculation: 4 multiplied by 3 multiplied by 2 equals 24 ways.
Total ways: Adding the two scenarios together, 12 plus 24 equals 36 ways.
Therefore, option B is the correct answer.
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