Dear experts,

I am going through Permutation and Combinations chapter from Magical Boo on Quicker Maths by M. Tyra. I have stumbled on the following points:

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

Total no. of selections of zero or more things from n identical thing = n+1

Total no. of selections of zero or more things from n different things = nC0 + nC1 + nC2 + nC3 +….nCn=(2)exp n

No. of ways to distribute (or divide) n identical things among r persons where any person may get any no of things = n+r-1Cr-1

Can anyone kindly refer me to a book on this subject or refer me to an article which can explain the above with an application or an example.

I am still in the process of going through this chapter for the second time, so most likely these are explained and I have not been able to associate these with the worked examples.

Kindly help

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for it should read

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/algebra/binomial-theorem.html

But don't hesitate to ask here.