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

How many $3$-digit numbers are there with no digit repeated?

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

There are $7$ men and $8$ women in a club. $A$ committee is formed using these persons. What will be the number of ways to select $6$ persons such that at least one is a woman?

Six objects $O_1$ to $O_6$ are arranged one on top of the other. In how many ways can these be arranged such that $O_1$ and $O_2$ are the $2$ bottom-most objects?

In how many ways can a cricket team of $11$ players be selected out of $16$ players,if $2$ particular players are always to be included?