If in a regular polygon the number of diagonals is $54$,then the number of sides of this polygon is

In how many ways can $6$ persons be selected from $4$ officers and $8$ constables,if at least one officer is to be included?

The number of ways in which any four letters can be selected from the word $CORGOO$ is

In a group of $6$ boys and $4$ girls,four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

There are $12$ volleyball players in all in a college,out of which a team of $9$ players is to be formed. If the captain always remains the same,then in how many ways can the team be formed?

The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word $'EXAMINATION'$ is