Question 10
Seven distinct awards are to be handed to seven students, one award per student, with one intended recipient for each award. Assume all $7!$ assignments are equally likely. The probability that every award goes to an incorrect recipient is $\frac ab$ in lowest terms. Find $a+b$. The corresponding probabilities with five and six awards are given as $\frac{11}{30}$ and $\frac{53}{144}$, respectively.
Enter one positive integer, without units.
Enter one positive integer, without units.