This is an equations that comes up quite commonly in algorithm analysis:
here is an intuitive understanding for this.
Assume we have 10 items.
And we need to find sum of all possible combinations of these
i.e. 0C10 + 1C10 + 2C10 .....
What we are doing is basically we have 10 positions and in that we have 10 elements (since its a combination order does not matter). And in each position we have a choice for the item to be included or Not-included. So its a binary choice for each position and since we have 10 positions its 2x2 10 times i.e. 2^10.
So for n positions we have 2^n possible ways we can select these items.
If you still want a further rephrasing of the same information you can read this : http://www.themathpage.com/aprecalc/permutations-combinations-2.htm#sum
Enjoy!
Assume we have 10 items.
And we need to find sum of all possible combinations of these
i.e. 0C10 + 1C10 + 2C10 .....
What we are doing is basically we have 10 positions and in that we have 10 elements (since its a combination order does not matter). And in each position we have a choice for the item to be included or Not-included. So its a binary choice for each position and since we have 10 positions its 2x2 10 times i.e. 2^10.
So for n positions we have 2^n possible ways we can select these items.
If you still want a further rephrasing of the same information you can read this : http://www.themathpage.com/aprecalc/permutations-combinations-2.htm#sum
Enjoy!
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