I have been searching in the web for books with logic demonstrations of equations, formulas, theorems, etc. The problem is, I have found them, but they include too much calculation. I would like to read a book where you can find an explanation and logical demonstrations of formulas, equations, etc. By this I mean, for example:
In the formula of permutation, is $n!$, because when you choose the first element, you only have left $n - 1$ elements, after when you choose the second, you have only left $n - 2$n, because you have already chosen 2 elements. This is what I want, a demonstration and logical explanation, to really understand a formula / theorem / equation, and not just replace variables.
So, could you recommend books? where there are logical explanations of many formulas?