Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.
What is the value of 33~ ?  Choose the correct option:
A) 31
B) 1
C) 2
D) 8
E) 0
n~ = (n-1)!   so 33~ = (33-1)= 
<gadget id="calculator">(33-1)</gadget>
<output>32</output>
32!   when 32!/33 we have 16*2 inside 32!   hence 33 gets cancelled and we get remainder as 0   0
<result>E</result>
Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.
What is the value of 33~ ?