The number of ways of dividing $200$ dissimilar things into $10$ groups each containing $20$ elements is

There are $4$ envelopes with addresses and $4$ corresponding letters. The probability that no letter goes into its correct envelope 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:

Three letters are dictated to three persons and an envelope is addressed to each of them. The letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.

In how many ways can a pack of $52$ cards be divided into four equal groups?

There are $4$ distinct colored balls and $4$ boxes of the same colors as the balls. In how many ways can the balls be placed in the boxes such that no ball goes into a box of its own color?