In how many ways can $6$ letters be posted in $5$ letter boxes available in the locality?

If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman,then the number of seating arrangements is

There are $5$ gentlemen and $4$ ladies to dine at a round table. In how many ways can they seat themselves so that no $2$ ladies are together?

There are $6$ multiple choice questions in an examination. How many sequences of answers are possible,if the first three questions have $4$ choices each and the next three have $5$ choices each?

If ${}^n{P_4} : {}^n{P_5} = 1 : 2$,then $n = $

There are $16$ points in a plane, out of which $6$ are collinear. How many lines can be drawn by joining these points?