https://www.gregmat.com/quizzes/quiz/timed-quant-practice-hard-section-2-sample-test-3 (Question 7)
I found a good insight about the derangement numbers.
the original formula is too long to remember but the estimation technique helps to scale it down.
N - Number of objects
D(N) - Number of derangements where N is the number of objects to be deranged. (Here it is 4)
e - euler’s number (approx 2.718)
D(N) = N! / e [Estimation formula]
D(1)= 0.36 (approx) = 0 (rounding)
D(2)= 0.735 (approx) = 1 (rounding)
D(3)= 2.207 (approx) = 2 (rounding)
D(4)= 8.830 (approx) = 9 (rounding)
D(5)= 44.150 (approx) = 44 (rounding)
following GRE rounding to nearest integer, we can quickly find the derangement number.