Lesson: GMAT Counting Strategies - Part II

Question link: https://gmatclub.com/forum/if-a-committee-of-3-people-is-to-be-selected-...
The problem is that you're including the selection of people who will not end up serving on the committee.

For example, let's change the question so that we select only 1 person (instead of 3 people) to be on the committee.
Using your approach, the solution would be as follows:
Stage 1: Select 1 person from couple A = 2 ways
Stage 2: Select 1 person from couple B = 2 ways
Stage 3: Select 1 person from couple C = 2 ways
Stage 4: Select 1 person from couple D = 2 ways
Stage 5: Select 1 person from couple E = 2 ways
Stage 6: Select 1 person from above 5 people = 5C1 ways
Total number of outcomes = (2)(2)(2)(2)(2)(5) = 160

Since we're really just selecting 1 person from 10 people, there are only 10 outcomes.

Does that help?

Question link: https://gmatclub.com/forum/how-many-ways-can-the-five-digits-3-3-4-5-6-b...

The MISSISSIPPI rule works only for situations in which there are no additional provisos. That is, the rule works if we are simply arranging objects where some of those objects are identical.
For this question we have the proviso that the "digit 3 must be separated by at least one other digit."
If this proviso weren't part of the question, then we could apply the MISSISSIPPI rule.