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:

There are $n$ different objects $1, 2, 3, \dots, n$ distributed at random in $n$ places marked $1, 2, 3, \dots, n$. The probability that at least three of the objects occupy places corresponding to their number is

$150$ students took admission. In how many ways can they be divided into three equal sections $A, B,$ and $C$?

There are $n$ letters and $n$ addressed envelopes. The probability that all the letters are not kept in the right envelope is:

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

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