Permutations, Combination and Binomial Expansion

If there are m distinct things

If there are m distinct things in Group 1 and n distinct things in Group 2, then selection of one thing from both groups can be done in (m + n) ways.

If the first operation can be

If the first operation can be done in m ways and second operation can be done in n ways, then two operations together can be done in (m × n) ways. The

The product of natural numbers from

The product of natural numbers from 1 to n is denoted as n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1. By definition, 0! = 1.

The number of ways to arrange

The number of ways to arrange r distinct objects from n distinct objects where order matters. Formula: nPr = n!/(n-r)!. Each arrangement is called a p

The number of ways to select

The number of ways to select r objects from n distinct objects where order doesn't matter. Formula: nCr = n!/[r!(n-r)!]. Each selection is called a co