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Permutations and combinations

Answer

$4$

Find permutations

$\,_{ \color{#FF6800}{ 4 } }P_{ \color{#FF6800}{ 1 } }$

$ $ Arrange the expression using $ \,_{n}P_{r} = \dfrac{n!}{\left(n-r\right)!}$

$\color{#FF6800}{ \dfrac { { \color{#FF6800}{ 4 } }! } { { \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) }! } }$

$\dfrac { { 4 }! } { { \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) }! }$

$ $ Subtract $ 1 $ from $ 4$

$\dfrac { { 4 }! } { { \color{#FF6800}{ 3 } }! }$

$\dfrac { { \color{#FF6800}{ 4 } }! } { { 3 }! }$

$ $ Express factorial in multiplication $ $

$\dfrac { \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } { { 3 }! }$

$\dfrac { 4 \times 3 \times 2 \times 1 } { { \color{#FF6800}{ 3 } }! }$

$ $ Express factorial in multiplication $ $

$\dfrac { 4 \times 3 \times 2 \times 1 } { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$

$\dfrac { 4 \times \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$

$ $ Do the reduction of the fraction for common parts $ $

$\color{#FF6800}{ 4 }$

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