The total no. of six digit numbers ${ x }_{ 1 }{ x }_{ 2 }{ x }_{ 3 }{ x }_{ 4 }{ x }_{ 5 }{ x }_{ 6 }$ having the property ${ x }_{ 1 }<{ x }_{ 2 }\le { x }_{ 3 }<{ x }_{ 4 }<{ x }_{ 5 }\le { x }_{ 6 }$, is equal to

Verify that: $^{15}C_{8}+^{15}C_{9}-^{15}C_{6}-^{15}C_{7} = 0$

The value of $\sum^{10}_{r=0}\begin{pmatrix}10\\r\end{pmatrix}\begin{pmatrix}15\\14-r\end{pmatrix}$ is equal to

If $^{n}C_{14} = ^{n}C_{16},$ find $^{n}C_{28}$.

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