i get confuse whether we have to use permutations or combinations in the word problems

Asked by Vidush | 25th Sep, 2013, 04:48: PM

Expert Answer:

Permutations are a way of counting arrangements:
Example : abc, acb, bac,bca, cab,cba are 6 different arrangements or permutations.
Combinations are a way of counting the number of groups.
Example: The 6 different arrangements above constitute one group or one combination.  
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
CombinationWhen 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."

Answered by  | 25th Sep, 2013, 10:44: PM

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