No. of selections of r things (r<=n) out of n identical things is 1

for it should read

No. of different selections of r things (r<=n) out of n identical things is 1

which is now perfectly true, for, there is no difference between the selections made. For if you line up 100 red identical balls and pick from the left numbers 1,3 and 5 or numbers 2,4 and 6 you will always have three identical red balls.

Now the next statement needs a similar qualification, for now you can pick only one ball, or two balls, or three balls and so on, and finally you can pick none at all. All of these selections are different - they differ by the number of balls from none to n and that makes n+1 selections in total.

Selections are usually termed permutations and the normal way of writing this nCk is using brackets containing the k below the n.

Now recommending a book is a bit difficult because I did all of this more than fifty years ago and in French. But you can Google the binomial theorem and Pascals Triangle like this one

http://www.mathsisfun.com/

But don't hesitate to ask here.