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Formula
Permutations and combinations
Answer
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$\,_{ 1 }C_{ 1 }$
$1$
Find a combination
$\,_{ \color{#FF6800}{ 1 } }C_{ \color{#FF6800}{ 1 } }$
$ $ Organize the equation using $ \,_{n}C_{r} = \dfrac{\,_{n}P_{r}{r!} = \dfrac{n!}{\left(n-r\right)!r!}$
$\color{#FF6800}{ \dfrac { { 1 }! } { { \left ( 1 - 1 \right ) }! { 1 }! } }$
$\dfrac { { 1 }! } { { \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) }! { 1 }! }$
$ $ Remove the two numbers if the values are the same and the signs are different $ $
$\dfrac { { 1 }! } { { \color{#FF6800}{ 0 } }! { 1 }! }$
$\dfrac { { 1 }! } { { \color{#FF6800}{ 0 } }! { 1 }! }$
$ $ 0! is 1 $ $
$\dfrac { { 1 }! } { \color{#FF6800}{ 1 } \times { 1 }! }$
$\dfrac { { 1 }! } { \color{#FF6800}{ 1 } \times { 1 }! }$
$ $ Multiplying any number by 1 does not change the value $ $
$\dfrac { { 1 }! } { { 1 }! }$
$\color{#FF6800}{ \dfrac { { 1 }! } { { 1 }! } }$
$ $ Since the numerator and the denominator are same, the value is 1 $ $
$\color{#FF6800}{ 1 }$
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