Problem
COM-B1-M03-P016 At Least One Multiple of \(5\)
#16
★★★☆☆ Level 3 of 5
How many \(4\)-element subsets of \(\{1,\ldots,20\}\) contain at least one multiple of \(5\)?
Subtract subsets with no multiples of \(5\).
Total: \(\binom{20}{4}=4845\). There are \(16\) numbers not divisible by \(5\), so subsets with no multiple of \(5\): \(\binom{16}{4}=1820\). Answer: \(3025\).
Complement method on subsets.