Evaluate (6!10!)/(8!8!)

$\frac{6! 10!}{8! 8!}$

Step 1

Rewrite $10!$ as $10 \cdot 9 \cdot 8!$ .

$\frac{6! (10 \cdot 9 \cdot 8!)}{8! 8!}$

Step 2

Cancel the common factor of $8!$ .

Cancel the common factor.

$\frac{6! (10 \cdot 9 \cdot 8!)}{8! 8!}$

Rewrite the expression.

$\frac{6! (10 \cdot 9)}{8!}$

$\frac{6! (10 \cdot 9)}{8!}$

Step 3

Rewrite $8!$ as $8 \cdot 7 \cdot 6!$ .

$\frac{6! (10 \cdot 9)}{8 \cdot 7 \cdot 6!}$

Step 4

Cancel the common factor of $6!$ .

Cancel the common factor.

$\frac{6! (10 \cdot 9)}{8 \cdot 7 \cdot 6!}$

Rewrite the expression.

$\frac{10 \cdot 9}{8 \cdot 7}$

$\frac{10 \cdot 9}{8 \cdot 7}$

Step 5

Cancel the common factor of $10$ and $8$ .

Factor $2$ out of $10 \cdot 9$ .

$\frac{2 (5 \cdot 9)}{8 \cdot 7}$

Cancel the common factors.

Factor $2$ out of $8 \cdot 7$ .

$\frac{2 (5 \cdot 9)}{2 (4 \cdot 7)}$

Cancel the common factor.

$\frac{2 (5 \cdot 9)}{2 (4 \cdot 7)}$

Rewrite the expression.

$\frac{5 \cdot 9}{4 \cdot 7}$

$\frac{5 \cdot 9}{4 \cdot 7}$

$\frac{5 \cdot 9}{4 \cdot 7}$

Step 6

Multiply.

Multiply $5$ by $9$ .

$\frac{45}{4 \cdot 7}$

Multiply $4$ by $7$ .

$\frac{45}{28}$

$\frac{45}{28}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{45}{28}$

Decimal Form:

$1.60714285 \dots$

Mixed Number Form:

$1 \frac{17}{28}$

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