The number of ways of dividing $200$ dissimilar things into $10$ groups each containing $20$ elements 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 number of arrangements of all digits of $12345$ such that at least $3$ digits will not come in their original positions 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

The number of ways in which $4$ letters can be put into $4$ addressed envelopes such that no letter goes into the envelope meant for it is:

The set $S = \{1, 2, 3, \dots, 12\}$ is partitioned into three sets $A, B, C$ of equal size such that $A \cup B \cup C = S$ and $A \cap B = B \cap C = C \cap A = \phi$. In how many ways can $S$ be partitioned?