5) In an examination hall there are 4 rows of chairs. Each row has 8 chairs one behind the other .there are 2 classes sitting for the examination and 16 students in each class. It is desired in a row all students of the same class should sit and that no two adjacent rows are allotted to the same class. In how many ways can 32 students can be seated?
a)2(16!*16!) b) (16!*16!) c) 2(16!+16!) d) (16!+16!)

Since there are 4 rows, let us label the rows as row 1,2,3,4.

each row has 8 chairs. since all the students of the same class sit in the same row. and no adjacent row is alloted to the same class.

therefore one class can be alloted either in 1 and 3 rows or 2 and 4 rows. therefore there are 2 ways to allot the rows to the class.

now 16 students of this class can be arranged in 16 seats, the number of ways to arrange 16 students in 16 seats=16!

similarly 16 students of other class can be arranged in 16! ways.

therefore total number of ways=2*16!*16! ways

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