Respuesta :
factorial 6 or 6! is 6*5*4*3*2*1, or 720.
factorial 3 times factorial 2 equals 3*2*1*2*1 or 3*2^2*1 or 12
factorial 3 times factorial 2 equals 3*2*1*2*1 or 3*2^2*1 or 12
You can use the fact that factorial of an integer can be evaluated by multiplying all the positive integers together from 1 to that number.
The answer to the given expression is
6! = 720
3!*2! = 12
How to evaluate factorial of a given positive integer?
Suppose we have to find the factorial of a given positive integer [tex]x[/tex]
Then we can evaluate it as:
[tex]x! = 1 \times 2 \times .... \times x\\\\\text{or writing it in reverse order}\\\\x! = x \times (x-1) \times (x-2) \times ... \times 3 \times 2 \times 1[/tex]
Remember the fact that 0! = 1 although you cannot write it in above expression (it is deduced by other method)
Using above definition to find the evaluated form of given expression
[tex]6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 30 \times 12 \times 2 = 360 \times 2 = 720\\6! = 720[/tex]
And
[tex]3! \times 2! = (3 \times 2 \times 1) \times (2 \times 1) = 6 \times 2 = 12\\3! \times 2! = 12[/tex]
Thus,
[tex]6! \neq 3!\times 2![/tex]
We have,
[tex]6! = 720\\3! \times 2! = 12[/tex]
Learn more about factorials here:
https://brainly.com/question/23464712
