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

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Which of the following is noth the number of ways of selecting `n` objects from `2n` objects of which `n` objects are identical
A. `2^(n)`
B. `("^(2n+1)C_(0)+^(2n+1)C_(1)+...+^(2n+1)C_(n))^(1//2)`
C. the number of possible subsets `{a_(1),a_(2),….,a_(n)}`
D. None of these


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Salim Ahmed Kawsar

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Correct Answer - D
`(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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