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A cinema hall has a capacity of 100 seats–40 seats in the balcony and 60 seats on the
ground floor. In how many ways can 100 viewers be accommodated, if 10 of them
want to be in the balcony and 15 others refuse to be in the balcony?
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The  cinema hall has a capacity of 100 seats

40 seats in the balcony in which 10 of them want to be in the balcony it means 10 seats are reserved

No of seats left in balcony : 30 seats

60 seats on the ground floor in which 15 others refuse to be in the balcony it means they want Ground floor

No of seats left in  ground floor 60 -15 = 45 seats

 15 ground floor and 10 Balcony seats are reserved

and only left 75 seats

therefore Total no of arrangements = (75)! / (45)! * (30)!
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