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anonymous
 one year ago
Combination question
anonymous
 one year ago
Combination question

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0In how many ways can the letters of the word NEWTON be arranged if they are used once only and taken 6 at a time, assuming, there is no distinction between the two Ns?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2well, newton has 6 letters so we start with 6! to account for the 2 duplicate n's, we divide by 2! so our answer is 6!/2!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Why do we divide by @! @Vocaloid? I don't get that :/

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2well, that's a bit tough to explain, maybe I can use a simpler example, let's say ABC and AAC for ABC, our possible arrangements are ABC, ACB, BAC, BCA, CAB, CBA, giving us 6 arrangements, or 6! for AAC, I can use the same pattern and get 6 arrangements, but because we have two A's, some of those arrangements are duplicated. our arrangements are AAC, ACA, AAC, ACA, CAA, CAA. there are 6 total, but only 3 of them are unique arrangements. we can get this result mathematically by dividing 3!/2! which gives us 6/2 = 3

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2so, basically, what I'm getting at is: if we have duplicate letters, you will end up getting repeat arrangements that get counted multiple times. in order to account for these, we divide by (number of repeat letters)! for each repeated letter I'm not great at explaining things, please let me know if you are still confused @Ahsome

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2[small typo in the first post, meant to say 3! instead of 6!]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I NOTICED :p No no no, that makes sense :) So, like if we had the question that we had the word PARALLEL. Do we use: \[\dfrac{8!}{3!}\]Cause the letter L is repeated 3 times?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2almost! you have a repeated L 3 times, but you also have a repeated letter A two times, so we do: 8! divided by (3!2!)

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2so, in the denominator, you need to include all the repeated letters

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0WHOOPS, forgot that :P So do we multiple the repetitions, like 3! times 2!, or add them?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much! :D How would this work for Permutations tho, where R and N aren't the same number? @Vocaloid?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2well, there's always the formula nPr = n!/(nr)!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I mean, how do we do that if we could have repetitions?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2can you clarify what you mean?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Like, imagine I had the word PARALLAL What are the combinations if I used those words to make a 3 letter word, without any repeats

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Does that make sense @Vocaloid?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2I understand the question, I'm just a bit uncertain on the answer

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2intuitively I would think 8P3/(3!2!) I'll get a second opinion though @ganeshie8

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I thought that aswell. Thanks so much @Vocaloid :D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Vocaloid, did you get it in the end?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2no response yet, sorry D: I need to go to sleep, tag someone if you still want a second opinion

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's cool. Thanks anyway @Vocaloid :D
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