Worked solution
Select three letters of ELEVEN without ordering them
Given that the order in which the letters of the word ELEVEN are selected does not matter, how many ways can 3 letters be selected?
CJC · Lecture · Self-Practice 4
Use the actual letter supplies
ELEVEN contains three E copies and one each of L,V,N. Three distinct types give selections. Two E copies and one of L,V,N give 3 more. Three E copies give 1.
How did this part go?
List the unordered selections to check the count
The 8 selections can be represented as EEE, EEL, EEV, EEN, ELV, ELN, EVN, LVN. These strings are just fixed-order names for multisets; rearranging their letters does not create a new selection. Thus 4+3+1=8, matching the printed answer. This explanation supplements the source answer.
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Common mistakes
The source asks for selections, not ordered three-letter codewords. Do not multiply each selection by 3!.