1. Highest power of a number in N!

2. Number of zeros in the factorial of a number

3. First non-zero digit in N!

4. First two non-zero digit in N!

5. Exercise

1. Permutation & Combination
(i) Introduction of Selection/Combination
(ii) Number of ways of selecting ‘r’ articles from ‘n’ distinct article
(iii) Number of ways of selecting ‘r’ articles from ‘n’ distinct articles if ‘k’ article is always included

2. Total Number of combination of ‘n’ different things taken one or more at a time

3. Selection from identical object/article
(i) The total number of ways of selecting one or more things from ‘p’ identical things of one type, ‘q’ identical things of another type, ‘r’ identical things of another type and ‘n’ distinct things

4. Factor theory concept

5. Exercise

6. Formation of geometrical figures
(i) Number of straight lines from given ‘n’ points
(ii) Number of straight lines from given ‘n’ points, out of them exactly ‘k’ points are collinear
(iii) Number of triangle from given ‘n’ points if no three of them are collinear
(iv) Number of polygon of ‘r’ sides from given ‘n’ points if no three of them are collinear
(v) Number of diagonal of a polygon of n sides

7. Chess board Concept

8. Grid based problem Concept
(i) Number of Rectangle
(ii) Number of Squares
(iii) Shortest path Concept

9. Exercise

1. Permutation or Arrangement
       (i) Number of ways in which ‘n’ different objects can be arranged

2. Exercise

3. Circular arrangement
       (i) When clockwise ↻ & anticlockwise ↺ arrangement are different then number of arrangement of n different things around a circle.
       (ii) When clockwise ↻ & anticlockwise ↺ arrangement are same: i.e. Formation of Garland then number of arrangement of n different things.

4. Exercise

5. Word/Number Formation
        (i) Formation of word
       (ii) Formation of number

6. Exercise

7. Rank of a word in dictionary

8. Exercise

1. Division & Distribuition of objects into Groups
        case(1) → (i) → (A)
Distinct object ━ Distinct Group
┃
(i) Group size Fixed
┃
(A) Group sizes are distinct

        case (1) → (i) → (B)
Distinct object ━ Distinct Group
┃
(i) Group size Fixed
┃
(A) Group sizes are equal

         case (1) → (i) → (C)
Distinct object ━ Distinct Group
┃
(i) Group size Fixed
┃
(C) Group sizes are mix of distinct & equal

        case (1) → (ii)

Distinct object ━ Distinct group
                                  ┃
(ii) Group size NOT fixed

case (2): Identical object ━  Distinct group

case (3): Distinct object ━ Identical group

case (4): Identical object ━ Identical groups

2. Exercise

1. Number of Integral Solution

2. Special cases of integral solution

3. Application of multinomial in permutation with repetition

4. Inclusion – Exclusion principle

5. De – arrangement concept