Question

Find the sum of ^npn ,^np1 ,^nco &^nc1​

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{^nP_n,\;^nP_1,\;^nC_0,\;^nC_1}$

$\underline{\textsf{To find:}}$

$\textsf{The sum of}$

$\mathsf{^nP_n,\;^nP_1,\;^nC_0,\;^nC_1}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{^nP_n+\;^nP_1+\;^nC_0+\;^nC_1}$

$\mathsf{=n(n-1)(n-2)....3.2.1+n+1+n}$

$\mathsf{=n!+2n+1}$

$\underline{\textsf{Answer:}}$

$\textsf{The sum of}$

$\mathsf{^nP_n,\;^nP_1,\;^nC_0,\;^nC_1}\,\textsf{is}$

$\mathsf{n!+2n+1}$

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