Question
Question: The value of P(n, 1) + \(\frac{P(n,2)}{2!} + \frac{P(n,3)}{3!} + ...... + \frac{P(n,n)}{n!}\) is equ...
The value of P(n, 1) + 2!P(n,2)+3!P(n,3)+......+n!P(n,n) is equal to –
A
2n
B
2n – 1
C
2n–1
D
2n + 1
Answer
2n – 1
Explanation
Solution
n
\end{matrix}}{\begin{matrix}
n–1
\end{matrix}} + \frac{\begin{matrix}
n
\end{matrix}}{\begin{matrix}
n–2
\end{matrix}} \times \frac{1}{\begin{matrix}
2
\end{matrix}} + \frac{\begin{matrix}
n
\end{matrix}}{\begin{matrix}
n–3
\end{matrix}} \times \frac{1}{\begin{matrix}
3
\end{matrix}} + ....... + \frac{\begin{matrix}
n
\end{matrix}}{\begin{matrix}
0
\end{matrix}} \times \frac{1}{\begin{matrix}
n
\end{matrix}}$$
= <sup>n</sup>C<sub>1</sub> + <sup>n</sup>C<sub>2</sub> +……..<sup>n</sup>C<sub>n</sub>
= 2<sup>n</sup> – <sup>n</sup>C<sub>0</sub> = 2<sup>n</sup> – 1