`n` different toys have to be distributed among `n` children. Find the number of ways in which these toys can be distributed so that exactly one child gets no toy.

Find the number of ways in which 5 distinct balls can be distributed in three different boxes if no box remains empty.

Find the number of ways in which 10 different diamonds can be arranged to make a necklace.

Find the number of ways in which the birthday of six different persons will fall in exactly two calendar months.

Six apples and six mangoes are to be distributed among ten boys so that each boy receives at least one fruit. Find the number ways in which the fruits can be distributed.

The number of ways in which 11 identical pencils can be distributed among 6 kids each receiving atleast one is

Find the total number of way in which n distinct objects can be put into two different boxes

Ten identical balls are distributed in 5 different boxes kept in a row and labeled A, B, C, D and E. The number of ways in which the ball can be distributed in the boxes if no two adjacent boxes remains empty

A double-decker bus carry (u+l) passengers, u in the upper deck and l in the lower deck. Find the number of ways in which the u+l passengers can be distributed in the two decks, if r(lt=l) particular passengers refuse to go in the upper deck and s(lt=u) refuse to sit in the lower deck.

There are 2 identical white balls, 3 identical red balls, and 4 green balls of different shades. Find the number of ways in which they can be arranged in a row so that at least one ball is separated from the balls of the same color.