CBSE Class 11-science Answered

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.  

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.

Permutation:

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."