Question

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?

Answer 1

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