Assume a and b are positive integers. Decide whether each statement is true or false.   (a!)b = ab!  

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degeneratecircle eNotes educator| Certified Educator

I'm not sure if `ab!` means multiply `a` and `b` and then compute the factorial of the product, as in `(ab)!,` ` ` or first compute the factorial of `b` and then multiply this by `a,`  as in ` ` `a(b!),` but either way the statement is false. Just try some small numbers to get a counterexample. Let `a=2,b=3.` Then

`(a!)b=(2!)*3=6,` and

`(ab)! =(2*3)! =6! =720,` while `a(b!)=2*(3!)=2*6=12.`

Since neither of the last two equals 6, the statement is false.