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$\,_{ 9 }C_{ 6 }$
$84$
Find a combination
$\,_{ \color{#FF6800}{ 9 } }C_{ \color{#FF6800}{ 6 } }$
$ $ Organize the equation using $ \,_{n}C_{r} = \dfrac{\,_{n}P_{r}{r!} = \dfrac{n!}{\left(n-r\right)!r!}$
$\color{#FF6800}{ \dfrac { { 9 }! } { { \left ( 9 - 6 \right ) }! { 6 }! } }$
$\dfrac { { 9 }! } { { \left ( \color{#FF6800}{ 9 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right ) }! { 6 }! }$
$ $ Subtract $ 6 $ from $ 9$
$\dfrac { { 9 }! } { { \color{#FF6800}{ 3 } }! { 6 }! }$
$\color{#FF6800}{ \dfrac { { 9 }! } { { 3 }! { 6 }! } }$
$ $ Simplify the formula containing the factorial $ $
$\color{#FF6800}{ \dfrac { 9 \times 8 \times 7 } { 3 \times 2 \times 1 } }$
$\dfrac { \color{#FF6800}{ 9 } \color{#FF6800}{ \times } \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } } { 3 \times 2 \times 1 }$
$ $ Calculate the value $ $
$\dfrac { \color{#FF6800}{ 504 } } { 3 \times 2 \times 1 }$
$\dfrac { 504 } { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$
$ $ Calculate the value $ $
$\dfrac { 504 } { \color{#FF6800}{ 6 } }$
$\color{#FF6800}{ \dfrac { 504 } { 6 } }$
$ $ Reduce the fraction to the lowest term $ $
$\color{#FF6800}{ 84 }$
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