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:

The number of ways of dividing $52$ cards amongst four players equally 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.

Choose the correct number of ways in which $15$ different books can be divided into $5$ heaps of equal number of books.

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?