 # sir ,What is the main difference between permutation & combination?

11 years ago

Dear hitesh,

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

All the best.

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Sagar Singh

B.Tech, IIT Delhi

11 years ago

Combination means selecting a particular number of things from a larger group of things. In this, the order of selection does not matter.

That is, if i select,

r,g,t,y,d

is equivalent to

t,y,r,d,g

as the order of selection does not matter.

Permutation means selecting a particula number of things from a larger groups of things and then re-arranging them. In this, the order of selection matters.

That is,

r,g,t,y,d

is not equivalent to

t,y,r,d,g

as re-arranging the alphabets a new permutation is formed.

So, the basic difference is that in combination there is not arrangement, while in permutation there is arrangement.

11 years ago

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