The value of the determinant\[\left| \begin{matrix} ^{n}{{C}_{r-1}} & ^{n}{{C}_{r}} & (r+1) & ^{n+2}{{C}_{r+1}} \\ ^{n}{{C}_{r}} & ^{n}{{C}_{r+1}} & (r+2) & ^{n+2}{{C}_{r+2}} \\ ^{n}{{C}_{r+1}} & ^{n}{{C}_{r+2}} & (r+3) & ^{n+2}{{C}_{r+3}} \\\end{matrix} \right|\] is

\[^{n}{{C}_{r-1}}{{+}^{n}}{{C}_{r}}{{+}^{n}}{{C}_{r+1}}\]

The value of the determinant\[\left| \begin{matrix} ^{n}{{C}_{r-1}

1.	The value of the determinant\[\left\| \begin{matrix} ^{n}{{C}_{r-1}} & ^{n}{{C}_{r}} & (r+1) & ^{n+2}{{C}_{r+1}} \\ ^{n}{{C}_{r}} & ^{n}{{C}_{r+1}} & (r+2) & ^{n+2}{{C}_{r+2}} \\ ^{n}{{C}_{r+1}} & ^{n}{{C}_{r+2}} & (r+3) & ^{n+2}{{C}_{r+3}} \\\end{matrix} \right\|\] is
A.	\[{{n}^{2}}+n-1\]
B.	0
C.	\[^{n+3}{{C}_{r+3}}\]
D.	\[^{n}{{C}_{r-1}}{{+}^{n}}{{C}_{r}}{{+}^{n}}{{C}_{r+1}}\]
Answer» C. \[^{n+3}{{C}_{r+3}}\]

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The value of the determinant\[\left| \begin{matrix} ^{n}{{C}_{r-1}} & ^{n}{{C}_{r}} & (r+1) & ^{n+2}{{C}_{r+1}} \\ ^{n}{{C}_{r}} & ^{n}{{C}_{r+1}} & (r+2) & ^{n+2}{{C}_{r+2}} \\ ^{n}{{C}_{r+1}} & ^{n}{{C}_{r+2}} & (r+3) & ^{n+2}{{C}_{r+3}} \\\end{matrix} \right|\] is

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