Theorems - Permutations and Combinations

1. n! = n[9n-1)!]

2. I fone thing can be done in m ways and after it has been done by anyone of these m ways, another thing cna be done in n ways, independent of the ways of dong the first thing, then the total number of ways doing the two things together is mn.

(Chapter : permutations and combinations)

Principle of Mathematical Induction

If a given open sentence involving n is true for n = 1 and its truth for n = kimplies its truth for n = k+1, then it is true for every natural number n

Theorem of Resolved Parts

The sum of the resolved parts of two forces acting through a point along any direction is equal to the resolved part of the resultant of the two forces along that direction.

Explanation

If you find the resolved parts in some direction initially and then find their resultant, it will be equal to the resolved part of the resultant of the two forces in the same direction.

(Topic: Vectors)