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

The number of diagonals in an octagon is:

How many different signals can be transmitted by arranging $3$ red,$2$ yellow and $2$ green flags on a pole? [Assume that all the $7$ flags are used to transmit a signal.]

There are $6$ men and $8$ women in a club. $A$ committee of $5$ people has to be formed. What will be the number of ways to select $5$ people if at least one woman is selected?

How many $3$-digit odd numbers can be formed from the digits $1, 2, 3, 4, 5, 6$ when
$(i)$ repetition of digits is not allowed
(ii) repetition of digits is allowed?

The number of four-letter words that can be formed using the letters of the word $BARRACK$ is