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It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. The number of words that contain exactly three different letters is? Sorry if it's confusing, but any kind of help would be really appreciated.

Thank you. Any helpful resources for discrete mathematics would also be appreciated. I'm writing this without looking at anyone else's number or solution technique first.

Combinatorics is a bit of an art, but the downside is that too much artfulness leads to different solutions. There is a certain freedom to thinking "Three, six, and seven are relatively small numbers, so let's brute force this! First, let's think about the number of ways to make a six-letter word out of the letters ABC, where each letter is used at least once. This is the number of surjections from six letter big words zero set Six Letter Big Words 01 with six elements to a set with three elements.

Six letter big words zero quantity in the bracket is a Strirling number of the second kind. You have to add the 3 cases in which the word is made of one single letter, not subtract them! This is an example of the inclusion-exclusion principle six letter big words zero work.

Note: I'm not sure this is the right answer since it disagrees with OP's calculation, so I'd appreciate it if someone would check six letter big words zero solution.

Once we've chosen the letters, we need to look at how to arrange them. Brute force is indeed rarely a solution, but when two answers differ, and the complexity is reasonable, it can prove one wrong The C code below counts in base 7 number of letters, in the "word" array count[6] and enumerates the number of cases where we have 4 kinds Six Letter Big Words Youtube of letters that are not used i.

Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Six letter big words zero What is Six Letter Big Words Questions Teams? Learn more. Asked 1 year, 3 months ago. Active 1 year, 3 months ago. Viewed 2k times. Matthew Daly Add a comment. Active Oldest Votes. Matthew Daly Matthew Daly Thank you for your simple explanation, I have previously done Stirling numbers, I'll keep it in mind to broaden my thinking in such ways.

And thank you for your kind formatting of my question. So you have subtracted the words made of 1 letter twice, and you have to add them back. Federico Poloni Federico Poloni 3, 16 16 silver badges 29 29 bronze badges. Thank you very much!

YiFan YiFan That's where our calculation differs. I am not able to understand the point of selecting 4 letters from a 6 letter word, which is made up of repetitions of 3 letters. I hope you get what I'm trying to say. Appreciate it though. Do let me know your thoughts if you can. What do you think?

Thanks for the effort! Kind of, lol. Not Six Letter Big Words Map yet well versed in computer programming, tbh. But I really appreciate that you took the time. And well, I thought using a bit of brute force, so to speak, could be a fun little brainstorm session for me.

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