SUB. :- MATHS, CHEMISTRY , BIOLOGY , PHYSICS

MONTH:- SEPTEMBER 2020

                The study of permutation and accumulation helps to determine how many different items can be sorted and selected differently from the total number of items given without actually making a list.  Some basic tricks will be useful in determining the arrangement of items or the number of types of selection.  The two basic principles for this calculation are as follows:

             Principle of Multiplication: (Basic Principle of Calculation)  The number of types of events occurring together in a given order is mx.  

         The principle of addition if one event E occurs differently from x and another event IF occurs differently from n.  Suppose the two events do not occur together, then the number of types of occurrence of event E or event “is n + n.

Example : 

(i) Out of the numbers between 99 and 1000, how many numbers have unit number 7? 

(2) Out of the numbers between 99 and 1000, how many numbers have at least one digit 7? 

 Solution: 

(i) First we will note that all the numbers between 99 and 1000 are three digit numbers.  Its unit number is 7.  The number in the second place can be any number from 0 to 9.  The point of the century can be any one of the 9 digits out of 1 to 9 digits.  Thus, from the basic principle of calculation, among the numbers between 99 and 1000, there are 10 x 9 = 90 numbers that have the number 7 in place of the unit.  

(2) Total numbers that have at least one digit 7 out of three digits = (Total numbers with three digits) – (Total numbers which do not have any 7 digits out of three digits).

  = (9 x 10 x 10) – (8 x 9 x 9)

 = 900 – 648 

= 252