AMC10 2027 - Self-practice Set 5 Question 6

Question 6

Al, Bill, and Cal are randomly assigned three distinct integers from $1$ through $10$, with all ordered assignments equally likely. What is the probability that Al's number is a multiple of Bill's and Bill's number is a multiple of Cal's?

$\frac9{100}$
$\frac1{90}$
$\frac1{80}$
$\frac1{72}$
$\frac2{121}$