### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Number of Divisions (Applications)

Let where are distinct primes & are natural numbers, then

1. The total no. of divisors of including is .
2. The sum of divisors is 3. Number of ways in which can be resolved as a product of two factors is Distribution of ‘ ’ balls into ‘ ’ boxes : ( ) : No restrictions. : Each box can contain at most one ball ( ). : each ball can contain at least one ball ( ). In the above 4 formulas are distincts.

Distribution of ‘ ’ identical balls into ‘ ’ distinct boxes : No restriction. : Each box contain at most one ball ( ). : Each box contain at least one ball ( ). Distribution of ‘ ’ identical balls into ‘ ’ identical boxes : No restriction.  : Each box contain at least one ball ( ). Distribution of ‘ ’ distinct balls into ‘ ’ identical boxes : No restriction.  : Each box contain at least one ball ( ). Scroll to Top