The diagram shows the seating plan for passengers in a minibus, which has 17 seats arranged in 4 rows. the back row has 5 seats and the other 3 row have 2 seats on each side. 11 passenger get on the minibus.

1. how many possible seating arrangements are there for the 11 passengers?

2. how many possible seating arrangements are there if 5 particular people sit in the back row?

It is given that there are 17 chairs all in all. In order to determine the possible arrangement for the 11 passengers we use the concept of basic principle of counting,

17 x 16 x 15 x 14 x 13 x ... x (17 - 11)

The answer to this item is 4.94 x 10^11

If five people are to sit in the back row, we take that 5 people as one group such that,

(5!) (12 x 11 x 10 x 9 x 8 x 7) = 79833600 ways