There are $4$ balls of different colors and $4$ boxes of the same colors as the balls. In how many ways can $2$ balls be placed in the boxes such that they do not match their respective colors?

In how many ways can $52$ cards be distributed equally among four players?

Three letters are to be sent to different persons,and addresses on the three envelopes are also written. Without looking at the addresses,the probability that all the letters go into the right envelopes is equal to

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:

There are $7$ greeting cards, each of a different colour, and $7$ envelopes of the same $7$ colours as the cards. The number of ways in which the cards can be put in envelopes, so that exactly $4$ of the cards go into envelopes of the respective colour, is:

The total number of ways of dividing $52$ cards amongst $4$ players,such that $3$ players have $17$ cards each and the fourth player has just $1$ card,is: