If \(A=\{1,2,3,4,5,6\}\) and \(B=\{0,1\}\), how many functions from \(A\) to \(B\) have exactly 3 inputs whose image is 1?

Correct answer: 20

Choose exactly 3 of the 6 inputs to map to 1; the remaining 3 inputs must map to 0. Hence, the number of functions is \(\binom{6}{3}=20\). The value 64 counts all functions from a 6-element set to a 2-element set, without fixing how many inputs map to 1. Exam tip: for a function into \(\{0,1\}\) with exactly \(r\) inputs mapping to 1, the count is \(\binom{n}{r}\).