The number of ways in which $5$ boys and $3$ girls can be seated in a row so that each girl is between two boys is:

$A$ question paper had ten questions. Each question could only be answered as True $(T)$ or False $(F)$. Each candidate answered all the questions. Yet,no two candidates wrote the answer in an identical sequence. How many different sequences of answers are possible?

$A$ father with $8$ children takes them $3$ at a time to the Zoological gardens,as often as he can without taking the same $3$ children together more than once. The number of times he will go to the garden is

The principal wants to arrange $5$ students on the platform such that the boy $SUNIL$ occupies the second position and such that the girl $GITA$ is always adjacent to the girl $NITA$. How many such arrangements are possible?

There are $10$ lamps in a hall. Each one of them can be switched on independently. The number of ways in which the hall can be illuminated is

Numbers greater than $1000$ but not greater than $4000$ which can be formed with the digits $0, 1, 2, 3, 4$ (repetition of digits is allowed),are