# Summary

- If a certain activity
*A*can be done in “*m*” different ways and another activity*B*can be done in “*n*” different ways, then the total number of ways of doing both*A***and***B*simultaneously or sequentially will be*m*×*n*. - If out of 2 activities, we are doing any one of them, which means either we shall do
*A***or**we shall do*B*, but not both, then the number of ways of doing either*A***or***B*will be*m*+*n*. - The product of first
*n*natural numbers is called*factorial n.*It is written as*n*! - The number of ways of arranging
*r*objects taken at a time from*n*objects is called permutations of*n*objects by taking*r*objects at a time. Mathematically, we write it asand it is defined as^{n}P_{r} - Permutations of
*n*things taken all at a time, out of which*p*things are alike of one kind and*q*things are alike of another kind is given by ways. - In circular permutations, if anticlockwise and clockwise order arrangements are considered distinct, then the number of circular permutations of
*n*objects is (*n –*1)!*.* - If anticlockwise and clockwise order of arrangements are not distinct, then the number of circular permutations of
*n*things are - The number of ways of selecting
*r*things from given*n*things are called combinations of*n*things by taking*r*things at a time. It is written as.^{n}C_{r } - The combinations of selecting
*r*_{1}objects from a set having*n*_{1}objects and*r*_{2}objects from a set having*n*_{2}objects, where combinations of*r*_{1}objects are independent from*r*_{2}objects is given by