There are 5 different coloured balls and 5 boxes of the same colour as that of balls the number of ways that exactly two balls will go to its same coloured boxes is

There are 5 different colour balls and 5 boxes of colours same as those of the balls. The number of ways in which one can place the balls into the boxes, one each in a box, so that no ball goes to a box of its own colour is

There are 5 different colour balls and 5 boxes of colours same as those of the balls. The number of ways in which one can place the balls into the boxes, one each in a box, so that no ball goes to a box of its own colour is

There are four balls of different colours and four boxes of colours same as those of the balls. Find the number of way in which the balls ,one in each box,of its own colour.

Let theta=(a_(1),a_(2),a_(3),...,a_(n)) be a given arrangement of n distinct objects a_(1),a_(2),a_(3),…,a_(n) . A derangement of theta is an arrangment of these n objects in which none of the objects occupies its original position. Let D_(n) be the number of derangements of the permutations theta . There are 5 different colour balls and 5 boxes of colours same as those of the balls. The number of ways in which one can place the balls into the boxes, one each in a box, so that no ball goes to a box of its own colour is

There are 4 balls of different colour and 4 boxes of colours the same as those of the balls. Find the number of ways to put one ball in each box so that only two balls are in boxes with respect to their colour.