Problem
COM-B1-M01-P019 Five Balls in Three Boxes
#19
★★★☆☆ Level 3 of 5
In how many ways can \(5\) identical balls be placed into \(3\) distinct boxes so that every box is nonempty?
First put one ball into each box.
After placing one ball in each box, \(2\) balls remain. Possibilities: both in one box — \(3\) ways; one in each of two boxes — \(3\) ways. Total: \(6\).
Without a heavy stars-and-bars formula.