Equals Times

Exercise 9.2

There exists in the isle of bile
A population of cats rather mild
Numbering "m" and each alone,
We start here with each cat at home.

Then each day there arrives another,
A new cat with a bit more bluster,
Making cat-friends with other cats,
But more often among those that are popular:

The chance that our cats become friends
Is the number of cat-friends our old cat has
Over all friendships on the island - plus a bit let's call "a."

Then, when time goes on and cats come in,
When we've got "t" more cats on this isle,
What's the chance that all have at least one friend?