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?

A. 15
B. 36
C. 48
D. 60

Explanation:

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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