In an election there are $8$ candidates,out of which $5$ are to be chosen. If a voter may vote for any number of candidates but not greater than the number to be chosen,then in how many ways can a voter vote?

How many different necklaces can be formed with $6$ white and $5$ red beads?

If the different permutations of the word $EXAMINATION$ are listed as in a dictionary,how many items are there in this list before the first word starting with $E?$

$n$ balls each of weight $w$ are weighed in pairs. The sum of the weights of all possible pairs is $120$. When they are weighed in triplets,the sum of the weights of all possible triplets is $480$. Then $n$ is:

The students in a class are seated according to their marks in the previous examination. Once,it so happens that four of the students got equal marks and therefore the same rank. To decide their seating arrangement,the teacher wants to write down all possible arrangements,one in each of separate bits of paper,in order to choose one of these by lots. How many bits of paper are required?

The value of ${2^n} \{ 1 \cdot 3 \cdot 5 \cdots (2n - 3) \cdot (2n - 1) \}$ is