All possible 3 digit numbers are formed using all the digits \(2,3,5,7,9\) without using any digit more than once. Among these 3 digit numbers, the number of numbers which are divisible by \(3\) but not divisible by \(5\) is
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For divisibility by \(3\), first identify valid digit combinations using the sum-of-digits rule. Then count permutations and separately remove those ending in \(5\) if divisibility by \(5\) is excluded.