Question

Permutations and Combinations

A double Decker bus can accommodate 80 passengers 35 in upper deck and 40 in lower deck. In how many ways can a group of 80 passengers be accommodated if 5 refuse to sit in the lower deck and 10 refuse to sit in the upper deck

Answer 1

Total seats = 80
In the Upper deck = 35
and in the Lower deck = 45

Number of ways of seating the particular 10 passengers in the lower deck = 45P10.
Number of ways of seating 5 particular passengers in the upper deck = 35P5.
In the remaining 65 seats 65 passengers are seated in 65P65 =65! Ways.

These three arrangements are independent of each other.

Answer = 45P10* 35P5* 65!

Answer 2

you did mistake in typing .
passenger accommodate in upper Decker = 35
passenger accommodate in lower Decker = 45

5 refuse to sit in lower Decker it means they sit must be in upper Decker .
10 refuse to sit in upper Decker it means they sit must be in lower Decker .

now , 35 people of upper Decker have been utilzed then upper Decker accommodate 35 - 5 = 30
and in lower Decker = 45 - 10 = 35

remaining ( 80 - 5 - 10) = 65 ,
we need to distribute 30 people in upper Decker and rest in lower Decker
e.g
no of ways of distribution = ⁶⁵C₃₀ * ³⁵C₃₅
= 65!/30! *35! *1
= 65!/30! *35!