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Permutations and combinations
$\,_{ 12 }C_{ 5 }$
$792$
Find a combination
$\,_{ \color{#FF6800}{ 12 } }C_{ \color{#FF6800}{ 5 } }$
 Organize the equation using $\,_{n}C_{r} = \dfrac{\,_{n}P_{r}{r!} = \dfrac{n!}{\left(n-r\right)!r!}$
$\color{#FF6800}{ \dfrac { { 12 }! } { { \left ( 12 - 5 \right ) }! { 5 }! } }$
$\dfrac { { 12 }! } { { \left ( \color{#FF6800}{ 12 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) }! { 5 }! }$
 Subtract $5$ from $12$
$\dfrac { { 12 }! } { { \color{#FF6800}{ 7 } }! { 5 }! }$
$\color{#FF6800}{ \dfrac { { 12 }! } { { 7 }! { 5 }! } }$
 Simplify the formula containing the factorial 
$\color{#FF6800}{ \dfrac { 12 \times 11 \times 10 \times 9 \times 8 } { 5 \times 4 \times 3 \times 2 \times 1 } }$
$\dfrac { \color{#FF6800}{ 12 } \color{#FF6800}{ \times } \color{#FF6800}{ 11 } \color{#FF6800}{ \times } \color{#FF6800}{ 10 } \color{#FF6800}{ \times } \color{#FF6800}{ 9 } \color{#FF6800}{ \times } \color{#FF6800}{ 8 } } { 5 \times 4 \times 3 \times 2 \times 1 }$
 Calculate the value 
$\dfrac { \color{#FF6800}{ 95040 } } { 5 \times 4 \times 3 \times 2 \times 1 }$
$\dfrac { 95040 } { \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$
 Calculate the value 
$\dfrac { 95040 } { \color{#FF6800}{ 120 } }$
$\color{#FF6800}{ \dfrac { 95040 } { 120 } }$
 Reduce the fraction to the lowest term 
$\color{#FF6800}{ 792 }$
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