In daily life, we use permutations and combinations a lot. For example, we want to go from Newyork to New Jersey and return by a different mode of transport; out of 16 cricket probables, there are a number of ways of choosing final eleven; there are a number of ways of choosing preliminary and main subjects for civil services exam; there are many ways guests can be seated on a dining table, and so on.We will try to learn the basics of Permutations and Combinations.We have covered the same in the pre algebra as well
Permutations and Combinations
Permutation: Each of the different arrangements which can be made by taking some or all of a number of given things or object at a time is called a permutation.In permutation order of appearance of things is taken into account.the following examples are taken from algebra problems .
Permutations Examples: The following six arrangement can be made with three distinct object taking two at a time ab,bc,cb ,ba,ac,ca .each of these arrangement is called a permutation.
Combination:
Each of the different groups or selections which can be made by taking some or all of a number of given things or object at a time is called a combination.In combination order of appearance of things is not taken into account.the following algebra answer examples explain this better.
Combination Examples: Following three groups can be made with three different objects taken two at a time. ab, bc ca here ab and ba are the same group.
Basics of Permutations and Combinations
1) Permutation mean arrangement.
2) Combination mean selection.
3) Fundamental principle of Counting:
a) Multiplication Rule: If a work is done only when all of a number of work are done then number of ways of doing that work is equal to the product of number of way of doing separate work.
b) Addition rule: If a work is done only when any one of a number of work is done , then number of way of doing that work is equal to sum of number of work of way of doing separate work.
4) n!= 1.2.3………………..n.
0! =1
5) Number of permutation of n different things taken r at a time is denoted by n!/n-r!
b) Number of permutation of n different things =n!
c) Number of permutation of n things , out of which p are alike and are of one type , q are alike and are of second type and rest are all different n!/p!q!
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Permutations Examples , Basics of Permutations and Combinations , Combination Examples