Quantitative aptitude (cpt)

Combination of n things= suppose you have 5 things

taking some or all at a time= taking any number of things is a separate combntn i.e. taking 1 or 2 or 3 like 4,5,12,13,14,15,23,24,25,34,35,45,123,124,125,234,235,345,1234,2345,12345 are the diff combntn,

Main diff between prmutation and combination is, in a  comb things appear once in any order ( comb is indepedent of order)  but in prmuttn diff order of things is diff permuttn. ( permttn is depedent of order)  i.e.1234 is one combntn but 1234,1243,2341,2341,3412,3421,4321,1432,1324,1423,1432 are diff permttn.

You take the formula to derive no. of permttn/combntn from your book.

Thank you for your reply

But I wish to know the meaning of the formula 2 to the power n -1.

First please explain why 2 is multiplied n times and what is the meaning of 'this includes the case where all are left so -1'

I wish to understand the formula and proof because it makes no sense to me.

Also, how would i differentiate this type of permutation from other ordinary permutations? The  question looks just like any other ordinary permutation problem, wherein if i don't use this formula my answer will be wrong.

Please explain. 

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