The simplest sequential description of the Ewens sampling formula is called the Chinese restaurant process. The first customer arrives and is seated at a table. After \(n\) customers have been seated, the next customer is seated alone with probability \(\alpha /(n+\alpha)\); otherwise, the newcomer selects one of the seated customers uniformly at random and sits at that table. Show that the configuration after \(n\) customers are seated is given by \(P_{n, \alpha}\). Hence deduce that customers seven and nine are seated together with probability \(1 /(\alpha(\alpha+1))\).