Combinations: in how many ways can 6 books be selected?

[jasons0801]

I'm just starting a Discrete Math class and we have covered Permutations and Combinations. The following question was asked in the Combinations chapter. I was thinking that it would just be 20_C_6 but that is wrong.

A gift certificate at a local bookstore allows the recipient to choose six books from the combined list of ten best selling fiction and ten best selling non fiction books. In how many ways can the selection of six books be made?

Thank you in advance.

 

[Deleted member 4993]

I'm just starting a Discrete Math class and we have covered Permutations and Combinations. The following question was asked in the Combinations chapter. I was thinking that it would just be 20_C_6 but that is wrong.

A gift certificate at a local bookstore allows the recipient to choose six books from the combined list of ten best selling fiction and ten best selling non fiction books. In how many ways can the selection of six books be made?

Thank you in advance.

How do you know it is wrong?

 

[jasons0801]

The book has the answer for the problem which is 177,100. The answer to 20_C_6 is 38760.

 

[Deleted member 4993]

The book has the answer for the problem which is 177,100. The answer to 20_C_6 is 38760.

As posted - you have the correct answer to the problem.

It could be:

The book is wrong ........ it has happened
and/or
You are not posting the problem correctly and completly
and/or
You are looking at the answer of a different problem.

 

[soroban]

Hello, jasons0801!


This is a strangely-worded problem.

If six books are chosen from twenty books, who cares if they are half fiction and half non-fiction?

The book has the answer for the problem which is 177,100.

$\displaystyle \text{Then there is a }serious\text{ error in the problem itself.}$

$\displaystyle \text{That answer comes from: }\:{25\choose6}$

 

[jasons0801]

I made a slight error in posting the question but I do not believe it changes the logical interpretation. I left out the word DIFFERENT (see below).

A gift certificate at a local bookstore allows the recipient to choose six books from the combined list of ten best selling fiction and ten best selling non fiction books. In how many DIFFERENT ways can the selection of six books be made?

I assured that I was looking at the proper answer which is 177,100. My guess is that the book is wrong unless anyone else can show how 177,100 is the answer.

Thank you,
Jason

 

[jasons0801]

Hello, jasons0801!


This is a strangely-worded problem.

If six books are chosen from twenty books, who cares if they are half fiction and half non-fiction?

The book has the answer for the problem which is 177,100.

$\displaystyle \text{Then there is a }serious\text{ error in the problem itself.}$

$\displaystyle \text{That answer comes from: }\:{25\choose6}$

I agree now that you mention it. You are told to choose from two different lists (fiction and non fiction) but the books (I'm assuming) would all have different titles no matter if they were off of one list or two. I'm not sure what they are getting at by mentioning the two lists.

Thank you for pointing out where the answer comes from.

 

[Deleted member 4993]

I made a slight error in posting the question but I do not believe it changes the logical interpretation. I left out the word DIFFERENT (see below).

A gift certificate at a local bookstore allows the recipient to choose six books from the combined list of ten best selling fiction and ten best selling non fiction books. In how many DIFFERENT ways can the selection of six books be made?

I assured that I was looking at the proper answer which is 177,100. My guess is that the book is wrong unless anyone else can show how 177,100 is the answer.

Thank you,
Jason

I was of course assuming you could choose a book only once. If you could choose six copies of the same book (possible - you may want to give those away or something). Then the answer would be 20^6 ( = 64,000,000). Those selections would be different from each other too.

 

[jasons0801]

I was of course assuming you could choose a book only once. If you could choose six copies of the same book (possible - you may want to give those away or something). Then the answer would be 20^6 ( = 64,000,000). Those selections would be different from each other too.

That puts an entirely different spin on the question. Whether you could choose a book only once is not defined.

In my opinion, this is a poor question and only serves to confuse students as they are trying to get a grasp on the subject matter.

 

[Han Zhe]

It's been a decade and more since the question was posted by Jasons, I have encountered the same question as Jasons did. And of course, my answer to the question would be the same as Jasons which is 38760. But looking at Jasons's problem I am confused as well. So long has passed, is there any justification for why the answer from the book is 177,100?

 

[Steven G]

Jasons answer was already stated to be correct.

soroban stated how to get the answer in your book. It turns out that ₂₅C₆=177,100

I guess the two types of books should have had 15 and 10 vs 10 and 10.

You got the correct answer. Good job!