### 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 ().

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