Hello frndz,
Today we will learn about Counting Methods..
:- If an object is to be chosen from a set of m objects and a second object is to be chosen from a different set of n objects, then there are mn ways of choosing both objects simultaneously.
For eg. Suppose the objects are items on a menu. If a meal consists of one entree and one dessert and there are 5 entrees and 3 desserts on the menu, So in how many different ways one can be ordered from the menu?
Solution: Lets take entrees are ABCDE and desserts are XYZ.
then ways are AX, AY, AZ, BX, BY, BZ, CX, CY, CZ, DX, DY, DZ, EX, EY and EZ.
total number of different ways : 15
(General Formula: total number of first objects * total number of second objects
i.e. 5*3 = 15)
:- A symbol that is often used with the multiplication principal is the factorial. It is defined as the product of all the integers from 1 to n i.e. n!
For eg. 2! = 2*1 ; 3! = 3*2*1 etc...
(Note: 0! =1! = 1)
:- A permutation is a selection process in which objects are selected one by one in a certain order (Order matters).
For eg. If k objects to be selected from a larger set of n objects, permutation is
(n,k) = n! / (n-k)!
:- A combination is a selection process in which objects are selected without regards to order.
For eg. If k objects to be selected from a larger set of n objects, combination is
(n,k) = n! / k!(n-k)!
Today we will learn about Counting Methods..
:- If an object is to be chosen from a set of m objects and a second object is to be chosen from a different set of n objects, then there are mn ways of choosing both objects simultaneously.
For eg. Suppose the objects are items on a menu. If a meal consists of one entree and one dessert and there are 5 entrees and 3 desserts on the menu, So in how many different ways one can be ordered from the menu?
Solution: Lets take entrees are ABCDE and desserts are XYZ.
then ways are AX, AY, AZ, BX, BY, BZ, CX, CY, CZ, DX, DY, DZ, EX, EY and EZ.
total number of different ways : 15
(General Formula: total number of first objects * total number of second objects
i.e. 5*3 = 15)
:- A symbol that is often used with the multiplication principal is the factorial. It is defined as the product of all the integers from 1 to n i.e. n!
For eg. 2! = 2*1 ; 3! = 3*2*1 etc...
(Note: 0! =1! = 1)
:- A permutation is a selection process in which objects are selected one by one in a certain order (Order matters).
For eg. If k objects to be selected from a larger set of n objects, permutation is
(n,k) = n! / (n-k)!
:- A combination is a selection process in which objects are selected without regards to order.
For eg. If k objects to be selected from a larger set of n objects, combination is
(n,k) = n! / k!(n-k)!
:- (n,k) = (n,n-k)
For eg. (5,2) = 10 = (5,3)
Okie guys, Keep practice on !!!
Er. Ankur Garg
garg.ankur6@gmail.com
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