The number of selection of $n$ objects from $2 n$ objects of which $n$ are identical and the rest are different, is

Number of ways of selection of $n$ objects from $2 n$ objects, where as $n$ objects are identical in out of $2 n$ objects. $n$ identical and no different object $=1$ ways $$ ={ }^{n} C_{0} $$ $n-1$ identical and 1 different object $=1 \times{ }^{n} C_{1}$ $n-2$ identical and 2 different object $=1 \times{ }^{n} C_{2}$ 0 identical and $n$ different objects $=1 \times{ }^{n} C_{n}$ $$ ={ }^{n} C_{0}+{ }^{n} C_{1}+{ }^{n} C_{2}+\ldots \ldots+{ }^{n} C_{n}=2^{n} $$