The value of { }^{16} C_{9}+{ }^{16} C_{10}-{ | vedclass

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(A) We use the property of combinations: ${ }^{n} C_{r} = { }^{n} C_{n-r}$.Applying this to the terms ${ }^{16} C_{6}$ and ${ }^{16} C_{7}$:${ }^{16}

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(A) We use the property of combinations: ${ }^{n} C_{r} = { }^{n} C_{n-r}$.Applying this to the terms ${ }^{16} C_{6}$ and ${ }^{16} C_{7}$:${ }^{16} C_{6} = { }^{16} C_{16-6} = { }^{16} C_{10}$${ }^{16} C_{7} = { }^{16} C_{16-7} = { }^{16} C_{9}$Substituting these into the original expression:${ }^{16} C_{9} + { }^{16} C_{10} - { }^{16} C_{6} - { }^{16} C_{7} = { }^{16} C_{9} + { }^{16} C_{10} - { }^{16} C_{10} - { }^{16} C_{9}$$= ({ }^{16} C_{9} - { }^{16} C_{9}) + ({ }^{16} C_{10} - { }^{16} C_{10}) = 0 + 0 = 0$.

The value of ${ }^{16} C_{9}+{ }^{16} C_{10}-{ }^{16} C_{6}-{ }^{16} C_{7}$ is

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