How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?

Combinatorics Course at Cheenta | Problem Discussion

This is a collection of some revision notes. They include topics discussed in first three sessions of Combinatorics Course at Cheenta (Faculty: Ashani Dasgupta).

combinatorics 1(work sheet)

• Study of symmetry in geometry is greatly facilitated by combinatorial methods
• There are 6 symmetries of an equilateral triangle (=3! permutations of 3 things)
• There are 8 symmetries of a square (8 out of 4! permutations of 4 things are used up)
• All 24 symmetries (including orientations) of a tetrahedron account for 4! permutations of 4 things
• Cycle notation helps in exploiting permutations
• Length of a cycle equals it's order
• Bijection Principle helps to count sets which are otherwise difficult to count.
• Number of non negative integer solutions of a + b + c + d = n is $\displaystyle{ \binom{n+3}{3}}$
• We use balls and bars technique to do this
• Partitions
• Conjugate Partitions and Ferrar's diagram
• Catalan Numbers