Question
Mon June 27, 2011 By:

how shall we come to know that which ouestion is to be solved by the formula of conbination and which is to be solved by using the formula of permutations?

Expert Reply
Mon June 27, 2011
Permutation
Suppose we want to find the number of ways to arrange the three letters in the word CAT in different two-letter groups where CA is different from AC and there are no repeated letters.

Because order matters, we're finding the number of permutations of size 2 that can be taken from a set of size 3. This is often written 3_P_2. We can list them as:

CA CT AC AT TC TA

Combination
When we want to find the number of combinations of size 2 without repeated letters that can be made from the three letters in the word CAT, order doesn't matter; AT is the same as TA. We can write out the three combinations of size two that can be taken from this set of size three:

CA CT AT
 
The essential difference between a permutation and a combination is:
"In a permutation, each object is considered to be distinct, whereas, in a combination, all objects are considered to be alike and indistinct."

In other words,
"A combination is simply a choice of objects, while a permutation is a rearrangement or (sometimes, a re-alignment) of the choice of objects."
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