1999 Corolla - Starting Problem

#1
I've 1999 corolla, and it's having starting problem ONLY during 1st start in morning. I've to try more than 10 times to get it started. Got the battery checked, it' good. What can we say about the starter? Since I only have this problem very first time I start, is it safe to assume starter and coil is ok? Otherwise why am I not having this problem at other times?
 
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