Question

Evaluate6! 5!____8! 2!Simple as much as possible

Answer 1

Step-by-step explanation

If n is a positive integer, n factorial denoted by n! is a product of all positive integers less than or equal to n.

`n!=n(n-1)(n-2)\cdot...\cdot(2)(1)`

For example:

`4!=4\cdot3\cdot2\cdot1=24`

In this case, we have:

`\begin{gathered} (6!\cdot5!)/(8!\cdot2!)=((6\cdot5\cdot4\cdot3\cdot2\cdot1)(5\cdot4\cdot3\cdot2\cdot1))/((8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1)(2\cdot1)) \\ (6!\cdot5!)/(8!\cdot2!)=(5\cdot4\cdot3)/(8\cdot7) \\ (6!\cdot5!)/(8!\cdot2!)=(5\cdot4\cdot3)/(4\cdot2\cdot7) \\ (6!\cdot5!)/(8!\cdot2!)=(15)/(14) \end{gathered}`Answer
`(6!\cdot5!)/(8!\cdot2!)=(15)/(14)`