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Permutations and combinations
Answer
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$10$
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!}$
$\color{#FF6800}{ \dfrac { { \color{#FF6800}{ 5 } }! } { { \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) }! { \color{#FF6800}{ 2 } }! } }$
$\dfrac { { 5 }! } { { \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) }! { 2 }! }$
$ $ Subtract $ 2 $ from $ 5$
$\dfrac { { 5 }! } { { \color{#FF6800}{ 3 } }! { 2 }! }$
$\color{#FF6800}{ \dfrac { { \color{#FF6800}{ 5 } }! } { { \color{#FF6800}{ 3 } }! { \color{#FF6800}{ 2 } }! } }$
$ $ Simplify the formula containing the factorial $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } }$
$\dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } } { 2 \times 1 }$
$ $ Calculate the value $ $
$\dfrac { \color{#FF6800}{ 20 } } { 2 \times 1 }$
$\dfrac { 20 } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$
$ $ Calculate the value $ $
$\dfrac { 20 } { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 20 } } { \color{#FF6800}{ 2 } } }$
$ $ Reduce the fraction to the lowest term $ $
$\color{#FF6800}{ 10 }$
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