Combinatorics and Permutations in Indian Mathematics

Vyavakalpa is the term used in Lilavati to refer to combinations.

Brahmagupta is widely regarded as the father of Indian combinatorics due to his significant contributions to the field.

The formula for calculating the number of permutations of n distinct objects is n!, where n! represents the factorial of n.

Krama is the term used in Indian mathematics to refer to permutations.

Bhaskara II developed the concept of the Pascal's triangle, which is a triangular array of binomial coefficients.

The formula for calculating the number of combinations of n distinct objects taken r at a time is nCr, where nCr represents the binomial coefficient.

Bhaskara II provided a systematic treatment of permutations and combinations in his work, the Lilavati.

Krama is the term used in Indian mathematics to refer to the arrangement of objects in a specific order.

Vyavakalpa is the term used in Indian mathematics to refer to the selection of objects without regard to order.

Brahmagupta developed the concept of the Catalan numbers, which are a sequence of natural numbers that occur in various combinatorial problems.

The formula for calculating the number of ways to arrange n distinct objects in a circle is (n-1)!, where (n-1)! represents the factorial of (n-1).

Brahmagupta provided a method for solving linear equations using permutations and combinations.

Samyoga is the term used in Indian mathematics to refer to the grouping of objects into subsets.

Brahmagupta developed the concept of the Fibonacci numbers, which are a sequence of numbers where each number is the sum of the two preceding ones.

Varga is the term used in Indian mathematics to refer to the division of a set of objects into equal parts.