INTRODUCTION:
We must have come across situations like.
choosing five questions out of eight questions in a question paper.
Whenever we go to a hotel we must come across situation like which items to be chosen from the menu card.
We discuss such situations in this chapter.
While learning ‘permutations and combinations' we should be in a position to clearly see whether the concept of permutation or the concept of combination is applicable in the given situation.
What is a combination?
In general a combination is only a selection.
Example: Forming a set with three elements using the digits 1,2,3,4,5 is a combination.
This involves only one process namely, selection of three elements say 2,4,5.
Then the element set formed is {2,4,5} which is same as the sets {5,4,2} {4,2,5} ect.
Thus, whenever there is no importance to the arrangement or order, but only a selection is required, then it is a combination.
What is permutation?
While a permutation involves two steps namely selection and arrangement.
Example: Forming a three digit number from the digits 1,2,3,4,5 is a ‘permutation'.
This involves two steps. In the first step we select the three digits say 2,4,5.
In the second step we arrange them to form a three digit number such as 245, 254, 542 etc.
Thus, whenever there is importance to the arrangement or order in which the objects are placed, then it is a permutation.
Key Concepts
To calculate the number of combinations and permutations we have to know
What is Factorial?
What is Fundamental Principle?
With out having any knowledge on the above two concepts we can not go further.
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