2 men and 1 women 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 can not sit on the seat reserved for ladies. In how may different ways can the

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Q: 73 (IAS/2005)
2 men and 1 women 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 can not sit on the seat reserved for ladies. In how may different ways can the five seats be occupied by these three passengers?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,1,8,3,1,4,1

keywords: 

{'passengers': [0, 0, 1, 0], 'seats': [6, 6, 8, 25], 'bus': [0, 0, 1, 1], 'seat': [2, 0, 2, 1], 'women': [9, 8, 22, 46], 'men': [4, 3, 12, 9], 'ladies': [0, 1, 2, 1], 'different ways': [0, 0, 5, 0], 'woman': [1, 0, 2, 5]}

The question involves arranging 3 passengers, 2 men and 1 woman, in 5 available seats with 1 of this seat reserved for women.

Option 1: In this setup, there would only be 15 ways for 3 people to occupy 5 seats, however, it doesn`t consider the rule where a man can`t sit in the seat reserved for ladies.

Option 2: The answer takes into account all possibilities of seating arrangement. The woman has 5 options of where to sit. The remaining 2 men then have 4 options for the first man and 3 options for the second, giving a total of 5*4*3 = 60. However, this includes cases where a man sits on the lady`s seat. Therefore, we must subtract these cases, which happens when one man sits first. This case gives us 1 (lady`s seat for the man) * 4 (any seat for the second man) * 4 (any seat for the woman), which is 1*4*4 = 16. Subtracting this from the initial 60 gives 60 - 16 = 44, not 36.

Alert - the correct answer should be 44.

Option 3 and 4