Problem
COM-B1-M04-P009 Subset and Element
#9
★★☆☆☆ Level 2 of 5
How many pairs \((S,x)\), where \(S\subset\{1,\ldots,6\}\) and \(x\in S\), are there?
First choose \(x\), then the remaining elements of \(S\).
Choose \(x\) in \(6\) ways. For each \(x\), each of the other \(5\) elements either belongs to \(S\) or not: \(2^5\) ways. Total: \(6\cdot2^5=192\).
Pair as the counted object.