Question

How can we know when to use + sign and when to use × while solving a combintion problem?

Answer 1

I think you're talking about in word problems. The general rule of thumb:

If it is referring to two events as an 'OR' scenario, you will use addition between the combinations for the two events

If it is referring to the two events as an 'AND' scenario, you will use multiplication between the two events.



It's best to try and use a Venn diagram if you are a visual person, to understand the total number of possible cases and how to find them. If you have any questions, or want an example, lmk

Answer 2

An example would be great. Thanks!

Answer 3

Okay, I came up with a scenario

You have a hat with 15 yellow marbles and 13 blue marbles.

1. How many ways can you make 3 yellow marbles AND 2 blue marbles
Here, you would do
\(\operatorname{nCr}\left(15,3\right)\cdot\operatorname{nCr}\left(13,2\right)\)

Alternatively...
2. 3 yellow marbles OR 2 blue marbles
\(\operatorname{nCr}\left(15,3\right)+\operatorname{nCr}\left(13,2\right)\)

Answer 4

and on a venn diagram

the AND scenario would look like this


the OR scenario would look like this



and this is of course, where the two events are nondisjoint