Evaluate: (7 ! * 5 !)/(6 ! * 3 !)

Expression: $\frac{ 7 ! \times 5 ! }{ 6 ! \times 3 ! }$

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

$\frac{ 7 \times 6 ! \times 5 ! }{ 6 ! \times 3 ! }$

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

$\frac{ 7 \times 6 ! \times 5 \times 4 \times 3 ! }{ 6 ! \times 3 ! }$

Cancel out the common factor $6 !$

$\frac{ 7 \times 5 \times 4 \times 3 ! }{ 3 ! }$

Cancel out the common factor $3 !$

$7 \times 5 \times 4$

Calculate the product

$140$