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?

Permutations and Combinations 24/08/2021

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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