Find the total number of elements that satisfy this condition: (n/3)=20

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Otis said:
I'd tried going in that direction, Eddy, but you didn't seem interested.

:(
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I'm interested Otis. I am. I'm all about studying math.
But , but I didn't understand your approach either
I can if you lead me, but that is asking too much of you maybe.
If you're ready I am. Let's take it from the beginning. I won't go to bed until I'm done or until you tell me to stop.
Dr Peterson said it is hard to find an example explained online of an exercise like this.
If you guide me I'll do it. Hand and paper.
 
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Otis said:
My approach is different.

We know that 3! is 6, so I would multiply both sides by 6 right away.

n!/(n-3)! = 120

The left-hand side may be simplified.

Let's look at an example, to see how it simplifies. Let n = 10.

10!/(10-3)! means (1*2*3*4*5*6*7*8*9*10)/(1*2*3*4*5*6*7)

After cancelling common factors, we get 8*9*10

Think about 8*9*10 with respect to symbol n. We can express 8*9*10 in terms of n. Can you see how?

The simplification is (n)(n-1)(n-2)

If you're not sure why, then write out more examples and cancel common factors until it becomes clear. Let n=8. Let n=9. Let n=12…

After simplifying the left-hand side, we can solve the equation by inspection.

Determine the prime factorization of 120, and go from there, remembering that we're looking for three consecutive Integers whose product is 120.

?
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I need to know the mathematical why of what I do.
Take me from the beginning.
 
eddy2017 said:
… I didn't understand your approach … I can [understand it] if you lead me, but that is asking too much of you maybe…
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Huh?!

I did lead you. I'd explained the beginning of my approach, and I'd provided a worked example for how to simplify the resulting factorial expression.

I'd also asked you to tell me why, if you found what I'd said confusing. Is that too much to ask of you?

:confused:
 
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what is wrong here, is this good or not, if i can use it drop me a hint and lead down your path, if it is not that your approach tell me and let me know what is wrong with that.
 
let's do it step by step, no matter if you need time. i know you might not have the time. let's make our messages worthwhile. explain me when you see me wrong.
you mentioned something about multiplying both sides by 6. where right here?, right after this step?.
 
Otis said:
Work through the suggestions that I provided to you, in post #7.

If that's too confusing, then please post why.

If n is an Integer, how do we use symbol n to express the two Integers that come before n?

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i did not read the 'if that is too confusing then post why.
but i did not know how to start your approach. just that. i did not know how to start. it is the first exercise i do about this.
i'll be better prepared to take others after this.
 
maybe this is what you advised.
1627689902583.png
when simplyfying the left side, i'm in doubt about if i can multiply 6 * 3!, can I? ( 18!)
 
it is not so hard as it seems innit, topsquark?
throw me a hint whne you have the time as to what to do next.
 
Otis said:
I don't understand why you're thinking about that multiplication, but 6*3! is 36.

[imath]\;[/imath]
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for you is easy cos you know it. my doubt was if i could multiply the 6 by the 3 factorial.
topsquark cleared up quick by saying 3*2*1=6
so i thought the two 6's would cancel out.
i mean, i did not think about doing the factorial like he did cos this is my first time doing this. So, now by you saying that, then they can't cancel out. i do 6 times 6 =36,
like this,
1627693628018.png
now, what comes now?.
this will be a model exercise for others i will do.
 
Now, Otis, according to you, I should multiply 3* 6
And topsquard said they cancel out

I'm confused now.
Read post #36
 
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