# Solve for: _{9} C_{3}

## Expression: $_{ 9 } C_{ 3 }$

Use $_{ n } C_{ k }=\frac{ n ! }{ k ! \times \left( n-k \right) ! }$ to expand the expression

$\frac{ 9 ! }{ 3 ! \times \left( 9-3 \right) ! }$

Use $n !=n \times \left( n-1 \right) !$ to expand the expression

$\frac{ 9 \times 8 \times 7 \times 6 ! }{ 3 ! \times \left( 9-3 \right) ! }$

Subtract the numbers

$\frac{ 9 \times 8 \times 7 \times 6 ! }{ 3 ! \times 6 ! }$

Cancel out the common factor $6 !$

$\frac{ 9 \times 8 \times 7 }{ 3 ! }$

Calculate the product

$\frac{ 504 }{ 3 ! }$

Calculate the factorial

$\frac{ 504 }{ 6 }$

Cancel out the common factor $6$

$84$

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