Binomial Theorems - Can Someone Please Explain What The Question Is Asking?

[JeffM]

@JeffM @Jomo I have a few questions:
1) How do I compute the (25 over 6)?
2) When I multiply these values, should I keep the exponents?
3) After multiplying these values, will it provide me with the m, n, and coefficient? Or, did we find the m and n earlier? (For reference, I said that m was 48 and n was 228. The worksheet is at the top of the page so that you can see what it says I need to find.)

We found m and n earlier. See my previous post.

I would keep the exponents in order to avoid an impossibly large numeral and to help with simplification later.

Jomo and I have slightly different styles of presentation: he prefers 4⁶ and 6¹⁹, and I slightly prefer 2³¹ and 3¹⁹. They make absolutely no difference in mathematical substance. Do you see why? You say tomato and I say potato or something like that.

Technically, leaving the binomial coefficient as you have it is fine. I suspect, however, that your teacher wants you to turn it into a numeral. I gave you a citation to the formula a while ago.

 

[Steven G]

25 over 6 = 25/6 = 4 1/4 or 4.24

Now if on the other hand you mean 25 choose 6, ie [math]\binom{25}{6}[/math], that is another story. Here is the general formula.

[math]\binom{n}{r} = \dfrac {n!}{(n-r)!*r!}[/math]
Now how did you get your answer if you could not compute 25 choose 6.

The answer is whatever you get AFTER multiplying the three factors together. If you do not multiply the three numbers then you are not doing as I asked.

 

[pka]

After multiplying the three terms together (used my calculator) would the final solution be -725401600 * 6^19? If so, would the 6 be the coefficient?

Check this link. It a most useful tool.

 

[Steven G]

I too agree with this large number that leaving it the way it is without simplifying might be the best way to go. However, I feel that JeffM and I do not think you know how to do the multiplication out so we have been pushing you to do so.

 

[knpoe03]

We found m and n earlier. See my previous post.

I would keep the exponents in order to avoid an impossibly large numeral and to help with simplification later.

Jomo and I have slightly different styles of presentation: he prefers 4⁶ and 6¹⁹, and I slightly prefer 2³¹ and 3¹⁹. They make absolutely no difference in mathematical substance. Do you see why? You say tomato and I say potato or something like that.

Technically, leaving the binomial coefficient as you have it is fine. I suspect, however, that your teacher wants you to turn it into a numeral. I gave you a citation to the formula a while ago.

I'm sorry, which one was the binomial coefficient?

 

[knpoe03]

I too agree with this large number that leaving it the way it is without simplifying might be the best way to go. However, I feel that JeffM and I do not think you know how to do the multiplication out so we have been pushing you to do so.

I'm sorry, I'm really trying my best with what little I know

 

[Steven G]

It doesn't matter the names of the factors. You just need to calculate the values of the three factors and multiply them together.

Since you asked I will answer your question. The binomial coefficient is the product of the three numbers you are asked to multiply.

Lets take this a bit slower. Please compute each of the following:

[math]\binom {25}{6}[/math]
4⁶

6¹⁹

Can you multiply them together?
Using your calculator can you multiply the three factors in one shot without writing down the intermediate values? Give it a try!

 

[knpoe03]

25 choose 6: [math]\dfrac {25}{(25-6)*6}[/math] = 25/114
4^6 = 4096
6^19 =

25/114 * 4096 *

=my calculator couldn't handle this
25 choose 6 * 4^6 * 6^19 = 442030530379197815193600

@Jomo

 

[Steven G]

25 choose 6: [math]\dfrac {25}{(25-6)*6}[/math] = 25/114
4^6 = 4096
6^19 =

25/114 * 4096 *

=my calculator couldn't handle this
25 choose 6 * 4^6 * 6^19 = 442030530379197815193600

@Jomo

I don't believe that your calculator could handle 25 choose 6 * 4^6 * 6^19 but not 25/114 * 4096 *

which is a smaller number.

Your last answer is correct! In calculating 25 choose 6 you had [math]\dfrac {25}{(25-6)*6}[/math] which is not the formula that I gave you. What happened to the factorial symbols, ! . Just because you do not understand something does not mean that you ignore them. Do you know what 25! means? Please respond back with your answer.

 

[knpoe03]

I don't believe that your calculator could handle 25 choose 6 * 4^6 * 6^19 but not 25/114 * 4096 *

which is a smaller number.

Your last answer is correct! In calculating 25 choose 6 you had [math]\dfrac {25}{(25-6)*6}[/math] which is not the formula that I gave you. What happened to the factorial symbols, ! . Just because you do not understand something does not mean that you ignore them. Do you know what 25! means? Please respond back with your answer.

Opps, I thought you were just trying to emphasize certain things. No, then I do not know what it means.

I have no explanation for my calculator. I don't mind if you believe me or not, because I know my truth.

 

[JeffM]

25 choose 6: [math]\dfrac {25}{(25-6)*6}[/math] = 25/114
4^6 = 4096
6^19 =

25/114 * 4096 *

=my calculator couldn't handle this
25 choose 6 * 4^6 * 6^19 = 442030530379197815193600

@Jomo

25 choose 6 cannot possibly be 25/114, which is less than 1. Surely there is at least one way we can arrange 6 objects chosen from 25 distinct objects.

You have been given TWO formulas

[MATH]n! = 1 \text { if } n = 0;\ n! = n * (n - 1)![/MATH]
Calculate n! for n = 1 through n = 5. See the pattern?

25 choose 6 is [MATH]{25}{6} = \dfrac{25!}{6! * (25 - 6)!}[/MATH]
Of course your calculator could not handle it. That is why we told you to do exponential notation. These numbers are huge.

Your calculator can handle [MATH]\dbinom{25}{6}[/MATH], particularly if you do a lot of cancelling first.

Dude, you were given links. You were given posts. You were given definitions. If you do not understand something SAY SO.

 

[knpoe03]

Dude, you were given links. You were given posts. You were given definitions. If you do not understand something SAY SO.

I'm saying that I DO NOT UNDERSTAND. My stomach has been in knots trying to not only figure out this problem, but also figure out all of the different concepts and links that have been thrown at me. Excuse me if I do not remember the name of something, if I mess up, whatever. I thought that I was doing what was asked of me, I didn't know that I made a mistake. How can I say that I don't understand something if I don't even know what I'm doing wrong?

I'm trying my best here. It's fine, I'm over it. Never mind, I no longer want help. Thank you for your time.

 

[Steven G]

Opps, I thought you were just trying to emphasize certain things. No, then I do not know what it means.

I have no explanation for my calculator. I don't mind if you believe me or not, because I know my truth.

It is not that I think that you are not telling me the truth but rather something got typed into the calculator wrong.

For any positive integer n, n! = 1*2*3*4....*n. So for example, 5! = 1*2*3*4*5 = 120

 

[JeffM]

What don't you understand?

What n! means? You were told the formula. All you have to do is plug in the numbers and do the arithmetic.

What [MATH]\dbinom{25}{6}[/MATH] means? You were told the formula. All you have to do is plug in the numbers and do the arithmetic.

Actually, you were told the formulas several times.

 

[Steven G]

What are getting so upset about? There is no need to get that way. JeffM and I (and others) are here to help you. As soon as I saw some frustration in you the first thing I wrote was that we should go slower. I asked you to compute exact computations and this worked as you did get the answer. Please understand that it is hard to tutor you without seeing you. I have been able to look at students and know exactly what part they did not understand but with doing this online it is difficult. Please work with us and understand that we are doing our best. Possibly it would have been better if only one person helped you but that did not happen.