permutations and combinations

when did we use permutations and when did we use combinations ? Isn't they are alike ?

jomel_taneca said:

when do we use permutations and when do we use combinations ? Aren't they are alike ?

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Permutations involve order. ​How many ways can we form a queue?
There is a class of twenty students. ​How many ways can we form a line of five of the students?
Answer: \(\displaystyle _{20}\mathcal{P}_5=\dfrac{20!}{15!}\)
Combinations involve content. ​How many ways can we form a committee?
There is a class of twenty students. ​How many ways can we form a committee of five of the students?
Answer: \(\displaystyle _{20}\mathcal{C}_5=\dbinom{20}{5}=\dfrac{20!}{(15!)(5!)}\).