Hello, kilgoretrout!

We don't need a lot of fancy formulas . . .

There are: . possible choices.A casting for a play is being held at the local high school's gymnasium.

There are a total of 20 actors of differing age groups that attended this casting call;

they included 5 children, 7 adults, and 8 seniors.

There are only 3 acting roles available for the play and the casting director

decided to fill these roles by randomly drawing 3 of the 20 actors' name from a box.

Assuming all 3 acting roles in the play are different, what is the probability

that 3 actors of the same age range were chosen for the play?

3 children: . ways.

. .

3 adults: . ways.

. .

3 seniors: . ways.

. .