A \(5\)-digit number is to be formed using \(5\) different numbers selected from \(1,2,3,4,5,6,7,8\) and \(9\). No digit may be used more than once in any \(5\)-digit number.
Find how many \(5\)-digit numbers can be formed.[1]
Find how many of these \(5\)-digit numbers are greater than \(50\,000\) and even.[3]
A team of \(9\) people is to be chosen from \(6\) doctors, \(4\) dentists and \(2\) nurses. Find how many possible teams include at least \(2\) doctors, at least \(2\) dentists and at least \(2\) nurses.[3]
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Answer:(a)(i) \(15\,120\) (ii) \(3780\) (b) \(116\)