Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.
What is the value of 30~ ?  Choose the correct choice from the following options.
A) 1
B) 0
C) 2
D) 8
E) 31
n~ = (n-1)!   so 30~ = (30-1)= 
<gadget id="calculator">(30-1)</gadget>
<output>29</output>
29!   when 29!/30 we have 16*2 inside 29!   hence 30 gets cancelled and we get remainder as 0   0
<result>B</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 30~ ?