Permutation
Permutation is basically called as a arrangement where order does matters.Here we need to arrange the digits , numbers , alphabets, colors and letters taking some or all at a time.It is represented as ^{n}P_{r}
1. ^{n}P_{r} = n! / (n-r)!
2. If from the total set of n numbers p is of one kind and q ,r are others respectively then ^{n}P_{r} = n! / p! × q! × r!.
3. ^{n}P_{n} = n!
Combination
Permutation vs Combination
In both the things main difference is of order .In permutation order matters while in combination it does not.
Basic Difference :
In Arrangements we have,
Total no. of arrangements = total no. of groups or selection × r!
where r is the no. of objects in each group or selection. So ^{n}P_{r} = ^{n}C_{r} × r!
Questions :
1. How many triangles can be formed with four points (A,B,C & D) in a plane ? It is given that no three points are col-linear(not comes in straight line).From the three points A,B and C have only one triangle with these points.
Sol:
Here in this question , Order of digit does not matter so it is a combination.
^{n}C_{r} = n!/ r! × (n-r)!
^{4}C_{3 }= 4!/3! × ( 4- 3)!
^{4}C_{3 }= 4!/3! × 1!
^{4}C_{3 }= 4!/3! × 1!
^{4}C_{3 }= 4
Or
2. How many number plates of 3 digit can be formed with four digits 1,2,3 and 4 ?
Sol:
Here, the order of arrangement of digits does matter.
^{n}P_{r} = n! / (n-r)!
^{n}P_{r} = 4! / (4-3)!
^{4}P_{3} = 4! / 1!
^{4}P_{3} = 4!
^{4}P_{3} = 24
Factorial Notation
To solve problem like this you must have the knowledge of factorial.Factorial is represented as like " ! ".The Factorial notation is :