Suppose a lot contains $2 n$ objects of which n are identical. The number of ways to select $n$ objects
out of these $2 n$ objects must be

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the number of possible subsets of the set ${a_{1}, a_{2}, \dots \dots, a_{n}}$

$2^{n}$

none of these

${(^{2 n + 1} C_{0} +^{2 n + 1} C_{1} + \dots +^{2 n + 1} C_{n})}^{1 / 2}$

answer is A, B, C.

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Detailed Solution

We can take the objects as:
0 identical and n distinct;
1 identical and n- 1 distinct;
2 identical and n-2 distinct;
and so on...

∴Total number of ways = $\sum_{r = 0}^{^{n}} C_{r} = 2^{n}$

Thus, (a) is true Number of possible subsets of a set containing n elements is $2^{n}$

Also, $^{2 n + 1} C_{0} +^{2 n + 1} C_{1} +^{2 n + 1} C_{2} + \dots +^{2 n + 1} C_{n} = 2^{2 n}$

Thus, (b) and (c) are also true.

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