The number of ways in which $6$ distinct rings can be worn on the $4$ fingers of one hand is:

If all the words,with or without meaning,are written using the letters of the word $QUEEN$ and are arranged as in an English dictionary,then the position of the word $QUEEN$ is (in $^{th}$)

The number of points,having both coordinates as integers,that lie in the interior of the triangle with vertices $(0,0)$,$(0,41)$,and $(41,0)$ is:

The number of ways in which $6$ men and $5$ women can dine at a round table if no two women are to sit together is given by

The number of $4$-digit numbers that can be formed from the digits $0, 1, 2, 3, 4, 5, 6, 7$ such that each number contains the digit $1$ is:

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is