Question

The number of selection of $n$ objects from $2n$ 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

Answer: (A)

Number of ways of selection of $n$ objects from $2n$ objects, where as $n$ objects are identical in out of $2n$ 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 $=1\times {}^n{C}_n$
$={}^n{C}_0+{}^n{C}_1+{}^n{C}_2+\dots \dots +{}^n{C}_n=2^n$