Someone you know is planning a wedding. they have still have decide on the place of the reception, the dj, and the caterer. they have narrowed it down to 2 reception halls, 3 djs, and 2 catering companies. how many arrangements are possible for this wedding?

So essentially, we have a choice of :

2 reception halls
3 DJs
2 catering companies.

In order to find the number of arrangements, you need to multiply those : 2*3*2=12- So they have 12 arrangements.

why?

Imagine those 3 Djs- they are three arrangements.
Now, they can play in one or the other hall -so in total it's 3 Djs in one hall and 3 in the other -that's 6.

And all of those 6 possibilities can be catered by one or the other company- making the possibilities twice as many, so it's 12 in total!