Question

The number of selection of \(n\) objects from \(2 n\) objects of which \(n\) are identical and the rest are different is
(A) \(2^{n}\)
(B) \(2^{n-1}\)
(C) \(2^{n}-1\)
(D) \(2^{n-1}+1\)

Answer 1

Ans: (A)
Hint: Ways of selections are
\(\mathrm{n}\) identical and no different \(=1\) way
\(n-1\) identical and one from different elements \(=1 \times n_{c_{1}}\)
0 identical rest from different \(=1 \times{ }^{n} \mathrm{C}_{n}\)
\(\sum=^{n} c_{0}+^{n} c_{1}+^{n} c_{2}+\ldots .+^{n} c_{n}=2^{n}\)

Answer 2

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