Question

Find $\mathbf{\prod }_{\mathbf{j}\mathbf{=}\mathbf{0}}^{\mathbf{4}}\mathbf{ }\mathbf{\text{!}}\mathbf{!}$

Short answer

The value of the product is 288.

Step-by-step solution

Determination of factorial of numbers

The product sigma gives the multiplication of all the numbers from lower limit to upper limit.

The factorial of 0 is given as:

0! = 1

The factorial of 1 is given as:

1! = 1

The factorial of 2 is given as:

2! = (2)(2-1)

2! = 2

The factorial of 3 is given as:

3! = (3) (3-1)(3-2)

3! = 6

The factorial of 4 is given as:

4! = (4)(4-1)(4-2)(4-3)

4! = 24

Determination of the value of the product

The value of the product is given as:

$\begin{array}{r}\prod _{j=0}^4 j!=(0!)(1!)(2!)(3!)(4!)\\ \prod _{j=0}^4 j!=\left(1\right)\left(1\right)\left(2\right)\left(6\right)\left(24\right)\\ \prod _{j=0}^4 j!=288\end{array}$

Therefore, the value of the product is 288 .