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

In how many different ways can the letters of the word '$JUDGE$' be arranged in such a way that the vowels always come together?

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

There are $3$ sections in a question paper and each section contains $5$ questions. $A$ candidate has to answer a total of $5$ questions,choosing at least one question from each section. Then the number of ways,in which the candidate can choose the questions,is

All possible numbers are formed using the digits $1, 1, 2, 2, 2, 2, 3, 4, 4$ taken all at a time. The number of such numbers in which the odd digits occupy even places is

There are seven candidates for $3$ posts. In how many ways can the posts be filled?