Question

The value of ${ }^n C_2+{ }^n C_3+\ldots+{ }^n C_n$ is

(A) $2^n-n$

(B) $2^n-1-n$

(C) $2^n+1+n$

(D) None of these

Answer 1

$\begin{array}{l}\text { } \because{ }^n C_0+{ }^n C_1+{ }^n C_2+{ }^n C_3+\ldots+{ }^n C_n=2^n \\\Rightarrow{ }^n C_2+{ }^n C_3+\ldots+{ }^4 C_n=2^n-{ }^n C_0-{ }^n C_1=2^n-1-n\end{array}$

So, The correct option will be (B).