State Mackey's restriction formula and Frobenius reciprocity for characters. Deduce Mackey's irreducibility criterion for an induced representation.

For $n \geqslant 2$ show that if $S_{n-1}$ is the subgroup of $S_{n}$ consisting of the elements that fix $n$, and $W$ is a complex representation of $S_{n-1}$, then $\operatorname{Ind}_{S_{n-1}}^{S_{n}} W$ is not irreducible.