Puzzle #178: Kittens

Kittens are so darling and so prone to disappearing. You have been busy trying to count them.

You know that four of them have black fur, four have grey fur, and three have white fur. Each kitten is of at least one of the three colours and maybe more.

One kitten is grey and white only.

One kitten is black, grey, and white.

If there is a kitten that is just of one colour, then there are two of them that are just that colour.

There are no kittens that are black and grey only.

How many kittens are there of each colour combination, and how many are there in total?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, November 2, 2016 at noon Pacific Time. I will post the answer shortly after.