Permutations, Combinations and multiplication principle

Here's my question:

An investor offers 8 high risk mutual funds, 7 medium risk and 10 low risk funds.

If you wwant to invest in 3 high risk, 4 medium risk and 3 low risk funds, how many ways can you do this?

I was thinking I need to do combination for each of the 3 (high, medium and low) then multiply the 3 answers. Any thoughts?

lizzpalmer said:

Here's my question:

An investor offers 8 high risk mutual funds, 7 medium risk and 10 low risk funds.

If you wwant to invest in 3 high risk, 4 medium risk and 3 low risk funds, how many ways can you do this?

I was thinking I need to do combination for each of the 3 (high, medium and low) then multiply the 3 answers. Any thoughts?

Click to expand...

Nice thinking.
To generalize, if you have x ways to do one thing and y ways to do some other COMPLETELY INDEPENDENT thing, then you xy ways to combine both things, right?
It's a very simple principle IF YOU ARE SURE THAT THE THINGS ARE COMPLETELY INDEPENDENT.
The ways you pick high-risk funds do not constrain the way you pick medium-risk funds so they ARE completely independent.

The different ways that you can pick 3 high-risk funds from 8 is determined by combination rather than permutation because order is irrelevant, right?
ANOTHER SIMPLE PRINCIPLE to distinguish between when to utilize permutation and when combination.

Principles and concepts are the key to understanding math. All the rest is technique.

Thank you so much! I thought I was on the right track but it's always nice to know I'm not completely in left field!

lizzpalmer said:

Thank you so much! I thought I was on the right track but it's always nice to know I'm not completely in left field!

Click to expand...

What's wrong with left field?

Those are the guys who hit it out of the park!!!