CORRECT!

Great Job! To figure this problem, we must use the formula:

D_{n =} n!( 1-(1/1!)+(1/2!)-(1/3!)+…+(-1)ⁿ(1/n!) ) .

In this problem, n=5 because there are 5 players or objects. This makes our calculation look like:

D_{5 =} 5!( 1-(1/1!)+(1/2!)-(1/3!)+(1/4!)-(1/5!) ) = 5!(1/2-1/6+1/120) = 120(44/120) = 44 .

So the correct answer is 44.

You have a good understanding of derangements, good luck on the test!