A \(6\)-digit number is to be formed using the digits \(0,1,2,3,4,5,6,7,8,9\). The \(6\)-digit number cannot start with \(0\). Each digit can be used at most once in any \(6\)-digit number. Find how many of these \(6\)-digit numbers are divisible by \(5\).[3]
The number of combinations of \((n+1)\) objects taken \(13\) at a time is equal to \(16\) times the number of combinations of \(n\) objects taken \(12\) at a time. Find the value of \(n\).[3]
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