Five letters are placed at random in five addressed envelopes. The probability that all the letters are not dispatched in the respective right envelopes is

There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls,one in each box,could be placed such that a ball does not go to the box of its own colour is

There are $8$ different coloured balls and $8$ bags having the same colours as that of the balls. If one ball is placed at random in each one of the bags,then the probability that $5$ of the balls are placed in the respective coloured bags,is

Consider a square matrix of order $5$ such that $a_{ij} = 0$ for all $i + j = 6$,where $a_{ij} \in \{0, 1\}$ for all $i, j$. In each row as well as in each column,there is only one non-zero element. Then,the number of such matrices is:

Three letters,to each of which corresponds an envelope,are placed in the envelopes at random. The probability that all the letters are not placed in the right envelopes is

There are $n$ letters and $n$ addressed envelopes. The probability that all the letters are not kept in the right envelope is: