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!