IIT JEE , AIEEE Forum - Mathematics , Algebra

santosh05

total no of combinations of n diff things taken one or more at a time is 2ⁿ -1

pl xpln

Werewolf

Suppose there are n things , now we can take first thing in two ways that is take it or don't take it, so n things can be taken in 2ⁿ ways but since we cant have the case when all things are not taken so we subrtact 1 from total ways so we get 2ⁿ-1

akshay.khare91

look if we select 1 form n that can be done in nC1 and if we select 2 it is
nc2 upto ncn

therefore no. of ways of selecting = nc1 +nc2+nc3------ncn

but we know that nc0 + nc1 + nc2 -----------ncn = 2^n

and here nC0 is missing and that is equal to 1

therefore nc1+ nc2 ---------------ncn = 2^n-1..

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