there is a set A of n elements.
now a subset B is formed from A
the set A is then reconstructed by replacing elements of B
now a subset C is formed from A
find the number of ways of selecting B and C so that B and C are non intersecting
623n
The reason is simple..
Every element of A can either be a part of B or C or neither...
1sir u missed answer by 1
3n -1
and
sir can u please explain the 3n thing more elaborately
i know it may be easy but i have difficulty in understanding it:
like in the no.of subsets in set
i always understand this thing
nC1+nC2+........+nCn
but not this argument
2*2*2*2.......
62I dont see why a -1 should be there! (except if they disallow both B and C to be empty.. which they dont seem to!)
btw each element can either be in B or in C or in neither..
In another logic..
you have to select r elements from n and then k elements from n-r
so the number of ways will be
nCr x n-rCk
the sum has to be taken over all values of r and k....
11http://targetiit.com/iit-jee-forum/posts/combination-2-12912.html
A similar problem
1thanx for the hint nishant sir...
first fixing r....
k varies from 0 to n-r
so it is
^{n}C_{r}\sum_{k=0}^{n-r}{{^{n-r}C_{k}}}
now r varies from 0 to n
\sum_{r=0}^{n}{^{n}C_{r}(2^{n-r})}
=3n