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

The number of ways of distributing $3$ dozen fruits (no two fruits are identical) to $9$ persons such that each gets the same number of fruits is

The number of ways of dividing $52$ cards amongst four players so that three players have $17$ cards each and the fourth player has just one card,is

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

Six cards and six envelopes are numbered $1, 2, 3, 4, 5, 6$. Cards are to be placed in envelopes such that each envelope contains exactly one card,no card is placed in the envelope bearing the same number,and the card numbered $1$ is always placed in the envelope numbered $2$. The number of ways this can be done 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: