Probability - Gravner -13

Question

A middle row on a plane seats $7$ people. Three of them order chicken $(C)$ and the remaining four pasta $(P)$. The flight attendant returns with the meals, but has forgotten who ordered what and discovers that they are all asleep, so she puts the meals in front of them at random. What is the probability that they all receive correct meals?

Comments

$\frac{1}{\frac{7!}{4!\times 3!}}$=$\frac{2.3}{5.6.7}=\frac{1}{35}$