1.

Which of the following is noth the number of ways of selecting n objects from 2n objects of which n objects are identical

Answer»

`2^(n)`
`("^(2n+1)C_(0)+^(2n+1)C_(1)+...+^(2n+1)C_(n))^(1//2)`
the number of POSSIBLE subsets `{a_(1),a_(2),….,a_(n)}`
None of these

Solution :`(d)` We can take `0` indentical and `n` distinct , `1` IDENTICAL and `n-1` distinct , `2` identical and `n-2` distinct and so on…
`:.` Total no. of solutions `=sum_(r=0)^(n).^(n)C_(r )=2^(n)`
No. of possible subsets of a set containing `n` elements is `2^(n)` and `.^(2n+1)C_(0)+^(2n+1)C_(1)+^(2n+1)C_(2)+...+^(2n+1)C_(n)=2^(2n)`


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