Permutations and Combinations:
When we talk about the concept of Permutation and Combination,the basic meaning of permutation is rearranging in an ordered fashion,and the combination means the selection of a number of things taking some or all of them at a time.The permutation and combination takes place on different types of objects. The permutation of a different object is the number of different ways they can be ordered i.e. which is first, second, third, etc. If you desire to choose some objects from a larger number of objects, the way you place the chosen objects is also important. When comes to combination, on the other hand, one does not consider the order in which objects were selected or placed, just which objects were selected.
Permutation:
Permutation has two types:
* Permutation with Repetition.
* Permutation without Repetition.
Permutation with Repetition:
When we have n different objects then we have n choices each time. And if we are in a position to choose object r from n objects, the permutations are
n * n * n…..(r times) = n r
P (n, r) = n r
Permutation without Repetition:
In permutation without Repetition, we have to reduce the number of available choices each time. When we have n different objects then we have to reduce 1 from the previous term for each time.
This is like n * (n-1) * (n-2)….
And if we are in a position to choose r objects from n objects, the combination is
P (n, r) = [(n!)/((n-r)!)]
Example:
In how many ways a man can put 4 balls in 3 bags.
Solution:
First ball can put in 3 ways.
Second ball can put in 3 ways.
Third ball can put in 3 ways.
Fourth ball can put in 3 ways.
So the 4 ball can put in 3 * 3* 3* 3 =34 = 81 ways.
Combination:
Combination has two types:
* Combination with Repetition.
* Combination without Repetition.
Combination with Repetition:
We need to do is alter our permutations formula to reduce it by how many ways the objects could be in order but the order is not important here.
C (n, r) = [(n!)/(r!(n-r)!)]
Combination without Repetition:
When we have n different objects and to select r objects with repetition we have a formula
C (n, r) = [(n+r-1)/(r!(n-r)!)]
Example:
Write all the combination of four balls taken one at a time.
Solution:
Here n=4 and r=1
4C1= [(4!)/(1!(4-1)!)]
4C1= [(4 * 3 * 2 *1)/(1 * 3!)]
4C1= [(4*3*2*1)/(1*3*2*1)]
4C1 = 4.
Hope you like the above example of Permutations and Combinations.Please leave your comments, if you have any doubts.
When we talk about the concept of Permutation and Combination,the basic meaning of permutation is rearranging in an ordered fashion,and the combination means the selection of a number of things taking some or all of them at a time.The permutation and combination takes place on different types of objects. The permutation of a different object is the number of different ways they can be ordered i.e. which is first, second, third, etc. If you desire to choose some objects from a larger number of objects, the way you place the chosen objects is also important. When comes to combination, on the other hand, one does not consider the order in which objects were selected or placed, just which objects were selected.
Permutation:
Permutation has two types:
* Permutation with Repetition.
* Permutation without Repetition.
Permutation with Repetition:
When we have n different objects then we have n choices each time. And if we are in a position to choose object r from n objects, the permutations are
n * n * n…..(r times) = n r
P (n, r) = n r
Permutation without Repetition:
In permutation without Repetition, we have to reduce the number of available choices each time. When we have n different objects then we have to reduce 1 from the previous term for each time.
This is like n * (n-1) * (n-2)….
And if we are in a position to choose r objects from n objects, the combination is
P (n, r) = [(n!)/((n-r)!)]
Example:
In how many ways a man can put 4 balls in 3 bags.
Solution:
First ball can put in 3 ways.
Second ball can put in 3 ways.
Third ball can put in 3 ways.
Fourth ball can put in 3 ways.
So the 4 ball can put in 3 * 3* 3* 3 =34 = 81 ways.
Combination:
Combination has two types:
* Combination with Repetition.
* Combination without Repetition.
Combination with Repetition:
We need to do is alter our permutations formula to reduce it by how many ways the objects could be in order but the order is not important here.
C (n, r) = [(n!)/(r!(n-r)!)]
Combination without Repetition:
When we have n different objects and to select r objects with repetition we have a formula
C (n, r) = [(n+r-1)/(r!(n-r)!)]
Example:
Write all the combination of four balls taken one at a time.
Solution:
Here n=4 and r=1
4C1= [(4!)/(1!(4-1)!)]
4C1= [(4 * 3 * 2 *1)/(1 * 3!)]
4C1= [(4*3*2*1)/(1*3*2*1)]
4C1 = 4.
Hope you like the above example of Permutations and Combinations.Please leave your comments, if you have any doubts.
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