Problem
COM-B2-M02-P003 At Least One Letter \(A\)
#3
★★☆☆☆ Level 2 of 5
How many words of length \(6\) over the alphabet \(\{A,B,C,D\}\) contain at least one letter \(A\)?
Count the complement: words without \(A\).
There are \(4^6\) words in total. Without \(A\), each position has \(3\) choices, so \(3^6\) words. The answer is \(4^6-3^6=4096-729=3367\).
This is complement counting before full inclusion-exclusion.