B, III only.
III is pretty easy.
The product of 20! will be even, so adding 21 to it makes it odd. Hence, not a product of 2.
I and II are a little trickier
The product of 20! will be divisible by 7 and 21, as both of those quantities can be pulled out of the factors of 20!. (i.e. 7 and 14*3 give us what we need) Adding 21 to 20! keeps those same factors, since 21 is divisible by both 7 and 21.
This means 7 and 21 are both factors of "20!+21" leaving only 2 as a non factor
III is pretty easy.
The product of 20! will be even, so adding 21 to it makes it odd. Hence, not a product of 2.
I and II are a little trickier
The product of 20! will be divisible by 7 and 21, as both of those quantities can be pulled out of the factors of 20!. (i.e. 7 and 14*3 give us what we need) Adding 21 to 20! keeps those same factors, since 21 is divisible by both 7 and 21.
This means 7 and 21 are both factors of "20!+21" leaving only 2 as a non factor



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