Question 5
Seven unique awards are to be handed to seven exceptional students, one award per student. The probability that every award goes to an incorrect recipient is $\frac ab$ in simplest form. Find $a+b$. You are given that the corresponding probabilities for five and six awards are $\frac{11}{30}$ and $\frac{53}{144}$.
**Probability convention:** Each award has a different intended recipient, and all one-to-one assignments are equally likely. Enter the integer $a+b$.
**Probability convention:** Each award has a different intended recipient, and all one-to-one assignments are equally likely. Enter the integer $a+b$.