MathDB
2021 Individual #25

Source:

April 28, 2022
2021 Individual

Problem Statement

Thelma writes a list of four digits consisting of 11, 33, 55, and 77, and each digit can appear one time, multiples time, or not at all. The list has a unique mode, or the number that appears the most. Thelma removes two numbers of that mode from the list; her list now has no unique mode! How many lists are possible? Suppose that all possible lists are unordered.
<spanclass=latexbold>(A)</span>18<spanclass=latexbold>(B)</span>24<spanclass=latexbold>(C)</span>30<spanclass=latexbold>(D)</span>36<spanclass=latexbold>(E)</span>48<span class='latex-bold'>(A) </span>18\qquad<span class='latex-bold'>(B) </span>24\qquad<span class='latex-bold'>(C) </span>30\qquad<span class='latex-bold'>(D) </span>36\qquad<span class='latex-bold'>(E) </span>48