How can I determing best combination of inputs?

Say I have 10 factors to test, and I want to determine the best combination of factors. I can't test every possible combination because I don't have the resources and the time.

I am thinking of testing each factor individually first. Then rank them from most effective to least effective. Then conclude that combining the top 3 would be more optimal than any other combination.

Is there anything wrong with this? If you think this is incorrect, can you please give an example with your explanation. Thanks.
 
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