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Formula
Permutations and combinations
$\,_{ 5 }C_{ 2 }$
$10$
Find a combination
$\,_{ \color{#FF6800}{ 5 } }C_{ \color{#FF6800}{ 2 } }$
 Organize the equation using $\,_{n}C_{r} = \dfrac{\,_{n}P_{r}{r!} = \dfrac{n!}{\left(n-r\right)!r!}$
$\color{#FF6800}{ \dfrac { { 5 }! } { { \left ( 5 - 2 \right ) }! { 2 }! } }$
$\dfrac { { 5 }! } { { \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) }! { 2 }! }$
 Subtract $2$ from $5$
$\dfrac { { 5 }! } { { \color{#FF6800}{ 3 } }! { 2 }! }$
$\color{#FF6800}{ \dfrac { { 5 }! } { { 3 }! { 2 }! } }$
 Simplify the formula containing the factorial 
$\color{#FF6800}{ \dfrac { 5 \times 4 } { 2 \times 1 } }$
$\dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } } { 2 \times 1 }$
 Calculate the value 
$\dfrac { \color{#FF6800}{ 20 } } { 2 \times 1 }$
$\dfrac { 20 } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$
 Calculate the value 
$\dfrac { 20 } { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ \dfrac { 20 } { 2 } }$
 Reduce the fraction to the lowest term 
$\color{#FF6800}{ 10 }$
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