Solve 1!*2!*3!*4!/7!

$$\frac { 1 ! \times 2 ! \times 3 ! \times 4 ! } { 7 ! }$$

Evaluate

$$\frac{2}{35}\approx 0.057142857$$

Solution Steps

The factorial of 1 is 1.

$$\frac{1\times 2!\times 3!\times 4!}{7!}$$

The factorial of 2 is 2.

$$\frac{1\times 2\times 3!\times 4!}{7!}$$

Multiply 1 and 2 to get 2.

$$\frac{2\times 3!\times 4!}{7!}$$

The factorial of 3 is 6.

$$\frac{2\times 6\times 4!}{7!}$$

Multiply 2 and 6 to get 12.

$$\frac{12\times 4!}{7!}$$

The factorial of 4 is 24.

$$\frac{12\times 24}{7!}$$

Multiply 12 and 24 to get 288.

$$\frac{288}{7!}$$

The factorial of 7 is 5040.

$$\frac{288}{5040}$$

Reduce the fraction \frac{288}{5040} to lowest terms by extracting and canceling out 144.

$$\frac{2}{35}$$

Factor

$$\frac{2}{5 \cdot 7} = 0.05714285714285714$$