![]() ![]() It's the method of legibly arranging from chaos. Permutation can be defined as the no of ways of arranging few or all members within a particular order. 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 anymore): The easiest way to explain it is to: assume that the order does matter (ie permutations), then alter it so the order does not matter. In other words, it is now like the pool balls question, but with slightly changed numbers. This is like saying “we have r + (n−1) pool balls and want to choose r of them”. It refers to the combination of N things taken from a group of K at a time without repetition. The combination is a process of selecting the objects or items from a set or the collection of objects, specified the order of selection of objects doesn’t matter. You can also check Difference Between Face Value and Place Value What is a Combination? the formula, for different notations, is: Without repetition, our choices get reduced each time. Here, we have to reduce the number of available choices each time. Which is easier to write down using an exponent of r: In other words, there are n possibilities for the first choice, THEN there are n possibilities for the second choice, and so on, multiplying each time. More generally: choosing r of something that has n different types, the permutations are: n × n × … (r times) When a thing has n different types … we have n choices each time! For example: choosing 5 of those things, the permutations are: It’s the method of legibly arranging from chaos. For example, the arrangement of objects or alphabets is an example of permutation, but selecting many objects or alphabets is an example of combination. The Difference between permutation and combination is that for permutation the order of the members is taken into consideration except for combination orders of members don’t matter.
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