Both of these terms means the number of different ways in which one can select the objects. Objects are not replaced and subsets are formed for their selection. If your selection order is a factor then we will call it a permutation and if it is not we call it a combination. On the other hand, a simple English language combination just comes with a simple meaning.
Alphabets are taken in a different way A, B, and C can be grouped, taken all at a time, are ABC, ACB, BCA, CBA, CAB, BAC.
Types of permutations
It has two types:
Repetition: eg 333
Non-repetition Like the first three people in the running race so you cannot be first or second in this case.
Permutations with repetitions
When a thing has n different types … we have n choices each time!
For example: choosing 3 of those things, the permutations are:
n × n × n
(n multiplied 3 times)
More generally: choosing r of something that has n different types, the permutations are:
n × n × … (r times)
(In other words, there are nn possibilities for the first choice, THEN there are nn possibilities for the second choice, and so on, multiplying each time.)
We have two types of combinations and there is no order in it.
Repetition is allowed
E.g the coins in your pocket (5,5,10,10)
Like lottery numbers which are really easy to understand and everyone has played it once in their lifetime. (13,32,23)
Combinations with repetition
They are the hardest to explain. Underlying factors are difficult to control and process in it. Combination calculations are not that difficult to make either.
Combinations without repetition
This is the exact case with the lottery. One number is drawn at a time and if you get the lucky numbers we win. The simplest and easiest way is to think that order does not matter and altering the order also doesn’t matter.
There is an easy way to work out how many ways “1 2 3” could be placed in order, and we have already talked about it. The answer is:
3! = 3 × 2 × 1 = 6
(Another example: 4 things can be placed in 4! = 4 × 3 × 2 × 1 = 24 different ways, try it for yourself!)
So we adjust our permutations formula to reduce it by how many ways the objects could be in order (because we aren’t interested in their order any more). When it comes to ordering the type, formulas and situations are different. Only knowing how these formulas work is really difficult. The real-world situation with both permutation and combination is another thing.
In the end, it’s difficult to do all these calculations and require a lot of struggle and an open mind. If you make one mistake the results will be horrible. If you find a problem while doing it all manually one can use the online permutation calculator for doing it.