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Formula
Permutations and combinations
Answer
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$$\,_{ 8 }C_{ 4 }$$
$70$
Find a combination
$\,_{ \color{#FF6800}{ 8 } }C_{ \color{#FF6800}{ 4 } }$
$ $ Organize the equation using $ \,_{n}C_{r} = \dfrac{\,_{n}P_{r}{r!} = \dfrac{n!}{\left(n-r\right)!r!}$
$\color{#FF6800}{ \dfrac { { \color{#FF6800}{ 8 } }! } { { \left ( \color{#FF6800}{ 8 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) }! { \color{#FF6800}{ 4 } }! } }$
$\dfrac { { 8 }! } { { \left ( \color{#FF6800}{ 8 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) }! { 4 }! }$
$ $ Subtract $ 4 $ from $ 8$
$\dfrac { { 8 }! } { { \color{#FF6800}{ 4 } }! { 4 }! }$
$\color{#FF6800}{ \dfrac { { \color{#FF6800}{ 8 } }! } { { \color{#FF6800}{ 4 } }! { \color{#FF6800}{ 4 } }! } }$
$ $ Simplify the formula containing the factorial $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \color{#FF6800}{ 6 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } } { \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } }$
$\dfrac { \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \color{#FF6800}{ 6 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } } { 4 \times 3 \times 2 \times 1 }$
$ $ Calculate the value $ $
$\dfrac { \color{#FF6800}{ 1680 } } { 4 \times 3 \times 2 \times 1 }$
$\dfrac { 1680 } { \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$
$ $ Calculate the value $ $
$\dfrac { 1680 } { \color{#FF6800}{ 24 } }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 1680 } } { \color{#FF6800}{ 24 } } }$
$ $ Reduce the fraction to the lowest term $ $
$\color{#FF6800}{ 70 }$
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