Question

Four slip of papers with the numbers $1,2,3,4$ written on them are put in a box. They are drawn one by one (without replacement) at random. In how many ways it can happen that the ordinal number of at least one slip coincide with its own number$?$

Answer 1

Total number of ways$=4!=24.$
The number of ways in which ordinal number of any slip does not coincide with its own number is the number of dearranqements of $4$ objects$=4!(\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!})=9$
Thus the required number of ways$=24-9=15$