Problem
COM-B2-M02-P010 Exactly Two Fixed Points
#10
★★★☆☆ Level 3 of 5
How many permutations of \(7\) elements have exactly \(2\) fixed points?
Choose the fixed points, then derange the rest.
First choose the \(2\) fixed points: \(\binom72=21\). The remaining \(5\) elements must have no fixed points, so they can be permuted in \(D_5=44\) ways. The answer is \(21\cdot44=924\).
Check that the student does not multiply by \(5!\).