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! / (nr)!
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 collinear(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! × (nr)!
^{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! / (nr)!
^{n}P_{r} = 4! / (43)!
^{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 :
37 videos53 docs148 tests

1. What is the difference between permutation and combination? 
2. How do you calculate the number of permutations? 
3. How do you calculate the number of combinations? 
4. Can you give an example of permutation? 
5. Can you give an example of combination? 
37 videos53 docs148 tests


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