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A reading list for a humanities course consists of 10 books,

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A reading list for a humanities course consists of 10 books, [#permalink] New post 16 Jan 2016, 03:00
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73% (01:53) correct 26% (02:48) wrong based on 115 sessions
A reading list for a humanities course consists of 10 books, of which 4 are biographies and the rest are novels. Each student is required to read a selection of 4 books from the list, including 2 or more biographies. How many selections of 4 books satisfy the requirements?

A 90

B 115

C 130

D 144

E 195

Practice Questions
Question: 11
Page: 332
Difficulty: medium/hard
[Reveal] Spoiler: OA

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Re: A reading list for a humanities course consists of 10 books, [#permalink] New post 16 Jan 2016, 03:09
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Solution

We do have 3 scenarios from which we can choose our books

4 biographies, so the probability is: \(1\)

3 biographies and 1 novel, so the probability is : \(\frac{4!}{3!1!}=4\) AND \(\frac{6!}{1!5!}=6\). Multiplying \(6*4=24\)

2 biographies and 2 novels, so the probabilty is : \(\frac{4!}{2!2!}=6\) AND \(\frac{6!}{2!4!}=15\). Multiplying \(15*6=90\)

Adding up : \(1+24+90=115\)

The answer is \(B\)
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Re: A reading list for a humanities course consists of 10 books, [#permalink] New post 04 Aug 2016, 15:17
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Attached is a visual that should help.
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Re: A reading list for a humanities course consists of 10 books, [#permalink] New post 01 Jul 2017, 17:33
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Good question and answer above, but if the test makers wanted to, they could ask this instead, which would make it a permutations question.

For example,

Given: 10 books on a book shelf, 4 are fiction books and 6 are biographies.

How many ways can a person select 4 books one-by-one from the shelf and have at least 2 of the books selected(out of the 4 books which they select in a specific order, one-by-one) be fiction books?

To illustrate what the question is asking, if you have a book shelf that has only 2 books, one of them a fiction book, like The Hobbit, and the other a biography, like Citizen Soldier, and ask how many ways can a person pick books from that book shelf so that they get The Hobbit as one of the two books they pick, then there are two different ways they could get The Hobbit as one of the two books they pick, 1) by picking The Hobbit first, then Citizen Soldier second, and 2) by picking Citizen Soldier first, then choosing The Hobbit second, so order would be significant when the a problem is stated as I have stated it in my example above.

This makes it a little more challenging, see if you can arrive at a solution if you would like to
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Re: A reading list for a humanities course consists of 10 books, [#permalink] New post 02 May 2018, 09:46
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Carcass wrote:
A reading list for a humanities course consists of 10 books, of which 4 are biographies and the rest are novels. Each student is required to read a selection of 4 books from the list, including 2 or more biographies. How many selections of 4 books satisfy the requirements?

 A 90
 B 115
 C 130
 D 144
 E 195


We can break this problem into scenarios:

Scenario 1: 2 biographies and 2 novels

The number of ways to select 2 biographies is 4C2 = 4!/[2! x (4 - 2)! = 4!/(2! x 2!) = (4 x 3)/2! = 6.

The number of ways to select 2 novels is 6C2 = 6!/[2! x (6 - 2)!]= 6!/(2! x 4!) =(6 x 5)/2! = 15.

So there are a total of 6 x 15 = 90 ways for this scenario.

Scenario 2: 3 biographies and 1 novel

The number of ways to select 3 biographies is 4C3 = 4.

The number of ways to select 1 novels is 6C1 = 6.

So there are a total of 4 x 6 = 24 ways for this scenario.

Scenario 3: 4 biographies

The number of ways to select 4 biographies is 4C4 = 1.

So there is only 1 way for this scenario.

So there are a total of 90 + 24 + 1 = 115 ways to choose 4 books that consist 2 or more biographies.

Answer: B
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Re: A reading list for a humanities course consists of 10 books, [#permalink] New post 07 Nov 2019, 21:08
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10 BOOKS ; Need to read 4 book. Case-->> 2 or more are bio. There are 3 step.

Step 1: 2 (bio) * 2 (novel) = 4C2 * 6C2 = 6 * 15 = 90
Step 2: 3 (bio) * 1 (novel) = 4C3 * 6C1 = 4 * 6 = 24
Step 3: 4 (bio) * 0 (novel) = 4C4 * 0C0 = 1 * 1 = 1 (Special case : 0C0 = 1)

Total : 90+24+1 = 115 (answer)
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Re: A reading list for a humanities course consists of 10 books, [#permalink] New post 19 Nov 2019, 08:44
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@carcass, Can you please fix the options.
The option selection is only showing option B.
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Re: A reading list for a humanities course consists of 10 books, [#permalink] New post 07 May 2020, 06:32
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Carcass wrote:
A reading list for a humanities course consists of 10 books, of which 4 are biographies and the rest are novels. Each student is required to read a selection of 4 books from the list, including 2 or more biographies. How many selections of 4 books satisfy the requirements?

A 90

B 115

C 130

D 144

E 195

Practice Questions
Question: 11
Page: 332
Difficulty: medium/hard


There are three possible cases to consider:
i) 2 biographies and 2 novels
ii) 3 biographies and 1 novel
iii) 4 biographies and 0 novels

i) 2 biographies and 2 novels
We can select 2 biographies from 4 biographies in 4C2 ways (= 6 ways)
We can select 2 novels from 6 novels in 6C2 ways (= 15 ways)
Total number of outcomes = (6)(15) = 90

ii) 3 biographies and 1 novel
We can select 3 biographies from 4 biographies in 4C3 ways (= 4 ways)
We can select 1 novel from 6 novels in 6 ways
Total number of outcomes = (4)(6) = 24

iii) 4 biographies and 0 novels
We can select 4 biographies from 4 biographies in 4C4 ways (= 1 way)
We can select 0 novels from 6 novels in 1 way
Total number of outcomes = (1)(1) = 1


TOTAL outcomes = 90 + 24 + 1 = 115

Answer: B

Cheers,
Brent

By the way, here's a video on mentally calculating combinations (like 6C2)

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Re: A reading list for a humanities course consists of 10 books, [#permalink] New post 22 Jun 2020, 00:38
Interesting methods!
Re: A reading list for a humanities course consists of 10 books,   [#permalink] 22 Jun 2020, 00:38
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