There are $3$ candidates for a post and one is to be selected by the votes of $7$ men. The number of ways in which votes can be given is

How many words can be formed out of the letters of the word '$EDUCATION$' such that vowels occupy the odd positions?

In a party,$12$ persons are to be arranged around a round table. If two particular persons are not to be seated side by side,then the total number of arrangements is

Suppose that $20$ pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar is connected by beams to the top of all its non-adjacent pillars,then the total number of beams is:

$\sum\limits_{r = 0}^m {^{n + r}{C_n} = } $

At an election,a voter may vote for any number of candidates,not greater than the number to be elected. There are $10$ candidates and $4$ are to be selected. If a voter votes for at least one candidate,then the number of ways in which he can vote is