Question
2 men and 1 woman board a bus of which 5 seats are vacant, one of these 5 seats is reserved for ladies. A woman may or may not sit on the seat reserved for ladies, In how many different ways can the five seats be occupied by these passengers?
Answer: Option B
CASE I IF LADY SITS ON THE RESERVED SEAT, THEN 2 MEN CAN OCCUPY SEATS FROM 4 VACANT SEATS IN = 4P2 = 4×3 = 12WAYS
CASE II IF LADY DOES NOT SIT ON REVERSED SEAT, THEN I. WOMAN CAN OCCUPY A SEAT FROM FOUR SEATS IN 4 WAYS. I. MAN CAN OCCUPY A SEAT FROM 3 SEATS IN 3 WAYS, ALSO I. MAN LEFT CAN OCCUPY A SEAT FROM REMAINING TWO SEATS IN 2 WAYS.
THEREFORE, TOTAL WAYS = 4X3X2 = 24WAYS
FROM CASE I AND CASE II
TOTAL NUMBER OF WAYS = 12+24 = 36
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CASE I IF LADY SITS ON THE RESERVED SEAT, THEN 2 MEN CAN OCCUPY SEATS FROM 4 VACANT SEATS IN = 4P2 = 4×3 = 12WAYS
CASE II IF LADY DOES NOT SIT ON REVERSED SEAT, THEN I. WOMAN CAN OCCUPY A SEAT FROM FOUR SEATS IN 4 WAYS. I. MAN CAN OCCUPY A SEAT FROM 3 SEATS IN 3 WAYS, ALSO I. MAN LEFT CAN OCCUPY A SEAT FROM REMAINING TWO SEATS IN 2 WAYS.
THEREFORE, TOTAL WAYS = 4X3X2 = 24WAYS
FROM CASE I AND CASE II
TOTAL NUMBER OF WAYS = 12+24 = 36
Was this answer helpful ?
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