Problem
COM-B1-M01-P023 No Letter Appears Exactly Once
#23
★★★★☆ Level 4 of 5
How many strings of length \(5\) over \(\{A,B,C,D\}\) have the property that no letter appears exactly once?
The possible multiplicities are \(5\) or \(3+2\).
If all \(5\) symbols are equal, there are \(4\) strings. If the multiplicities are \(3\) and \(2\), choose the letter appearing \(3\) times: \(4\) ways, the letter appearing \(2\) times: \(3\) ways, and the positions of the first letter: \(10\) ways. Total: \(4+4\cdot3\cdot10=124\).
Trains classification of possible object types.