Question

There are 10 seats in a dubble dacker bus , 6 in the lower deck and 4 on the upper deck. Ten passengers board the bus, of them 3 refuse to go to the upper deck and 2 insist on going up. The number of ways all the passengers can be seated is

a. 60

b. 10

c. 100

d. n.o.t.

Ans. D

Answer 1

Three persons are already fixed in lower deck and two in upper deck.
So for six seats there are 3 persons and for four seats there are 2 persons
And for the remaining 5 seats there are 5 persons.
Six seats there are 3 persons = ⁶P₃
And four seats there are 2 persons = ⁴P₂
And five persons are in five seats = ⁵P₅
So the number of arrangement are ⁶P₃₊⁴P₂+ ⁵P₅