Question

2 men and 1 women board a bus in which 5 seats are vacant. One of these five seats is reserved for ladies. A women 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 many different ways can the five seats occupied by these passengers?  

(a) 15 (b) 36 (c) 48 (d) 60

Answer 1

(b) There can be two cases :

(i) Lady occupies the reserved seat

(ii) Lady does not occupy the reserved seat.

Fixing one seat for the lady, 1st man can occupy any of the remaining 4 seats in four ways and the 2nd man occupy any of the remaining 3 seats in three ways. 

Hence, no of ways = 1 × 4 × 3 = 12

Leaving the reserved seat, 1st man can occupy any of the 4 seats in four ways. 2nd man can occupy any of the remaining 3 seats in three ways. Lady can occupy any of the remaining 2 seats in two ways. 

Hence, no of ways = 4 × 3 × 2 = 24 Thus, 

Total no of ways = 12 + 24 = 36