Problem
COM-B1-M02-P019 Two \(A\)'s Not Adjacent
#19
★★★☆☆ Level 3 of 5
How many words of length \(5\) over \(\{A,B,C,D\}\) contain exactly two \(A\)'s, and they are not adjacent?
First choose two non-adjacent positions for the \(A\)'s.
There are \(10\) pairs of positions for the two \(A\)'s. Adjacent pairs: \(4\), so non-adjacent pairs: \(6\). The remaining \(3\) positions can be filled independently with \(B,C,D\): \(3^3=27\). Answer: \(6\cdot27=162\).
Local position restriction.