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A reading list for a certain course consists of 10 books, of which 4 a 13 May 2015, 03:53
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B
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A reading list for a certain course consists of 10 books, of which 4 are poems and the rest are novels. Each student is required to read a selection of 4 books from the list, including at most 2 novels. How many selections of 4 books satisfy the requirements?

A. 90
B. 115
C. 130
D. 144
E. 195


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A reading list for a certain course consists of 10 books, of which 4 a 13 May 2015, 05:00
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Can be selected as

Case 1 PPNN 2 Poems out of 4 and 2 Novels out of 6 i.e. 4C2 * 6C2 = 90
or
Case 2 PPPN 3 Poems out of 4 and 1 Novels out of 6 i.e 4C3 * 6C1 = 24
or
Case 3 PPPP 4 Poems out of 4 i.e. 4C4 =1

Total no. of selections case 1 + case 2+ case 3 = 90 + 24 +1 = 115

So answer must be B. 115
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A reading list for a certain course consists of 10 books, of which 4 a 01 May 2018, 05:52
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A reading list for a certain course consists of 10 books, of which 4 are poems and the rest are novels. Each student is required to read a selection of 4 books from the list, including at most 2 novels. How many selections of 4 books satisfy the requirements?

A. 90
B. 115
C. 130
D. 144
E. 195


Total - restriction =

= (4 books out of 10) - ((3 novels and 1 poem) + (4 novels and 0 poems)) =

\(= C^4_{10} - (C^3_6*C^1_4 + C^4_6) =\)

\(= 210 - (20*4 + 15) = 115\).


Answer: B
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A reading list for a certain course consists of 10 books, of which 4 a 13 May 2015, 07:25
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Possibilities include
1novel, 3 poems
6! / 1!5! × 4! /3! 1! =24

2 novels, 3 poems
6!/2! 4! × 4!/2! 2! =90

0 novels, 4 poems
=1

24+90+1=115

B. 115
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A reading list for a certain course consists of 10 books, of which 4 a 13 May 2015, 11:18
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Novel=N,Poem book=P; therefore 10=4+Novels =>N=6;P=4

The final selection would be = 2N and 2P +1N and 3P + 4P =6C2*4C2 + 6C1*4C3 + 4C4 = 90+24+1=115

Hence answer is B

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A reading list for a certain course consists of 10 books, of which 4 a 14 May 2015, 06:12
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Bunuel
A reading list for a certain course consists of 10 books, of which 4 are poems and the rest are novels. Each student is required to read a selection of 4 books from the list, including at most 2 novels. How many selections of 4 books satisfy the requirements?

A. 90
B. 115
C. 130
D. 144
E. 195

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Options with two novels: 6C2 * 4C2 = 90

Options with one novel: 4C3 * 6C1 = 24

Option with no novel: 4C4 = 1

so 90+24+1 = 115

Answer is B
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A reading list for a certain course consists of 10 books, of which 4 a 15 May 2015, 09:49
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Bunuel
A reading list for a certain course consists of 10 books, of which 4 are poems and the rest are novels. Each student is required to read a selection of 4 books from the list, including at most 2 novels. How many selections of 4 books satisfy the requirements?

A. 90
B. 115
C. 130
D. 144
E. 195

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Required selection=(4C2*6C2)+(6C1*4C3)+(4C4)
=90+24+1
=115
Answer B
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A reading list for a certain course consists of 10 books, of which 4 a 31 May 2017, 19:02
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Bunuel
A reading list for a certain course consists of 10 books, of which 4 are poems and the rest are novels. Each student is required to read a selection of 4 books from the list, including at most 2 novels. How many selections of 4 books satisfy the requirements?

A. 90
B. 115
C. 130
D. 144
E. 195
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We are given that a course reading list contains 4 poems and 6 novels. We need to determine the number of ways a student can select 4 books if at most 2 novels can be selected.

Scenario one: 4 poems are selected.

4 poems can be selected in 4C4 = 1 way.

Scenario two: 1 novel and 3 poems are selected.

3 poems can be selected in 4C3 = 4!/[3!(4-3)!] = (4 x 3 x 2)/3! = 4 ways, and 1 novel can be selected in 6C1 = 6 ways.

Thus, 3 poems and 1 novel can be selected in 4 x 6 = 24 ways.

Scenario three: 2 novels and 2 poems are selected.

2 poems can be selected in 4C2 = 4!/[2!(4-2)!] = (4 x 3)/2! = 6 ways, and 2 novels can be selected in 6C2 = 6!/[2!(6-2)!] = (6 x 5)/2! = 15 ways.

Thus, 2 poems and 2 novels can be selected in 6 x 15 = 90 ways.

All 4 books with at most 2 novels can be selected in 1 + 24 + 90 = 115 ways.

Answer: B
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A reading list for a certain course consists of 10 books, of which 4 a 01 May 2018, 11:01
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Bunuel
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
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Total: 4B and 6N
Possible outcomes (2B,2N) + (3B,1N) + (4B)
4!/2!*2! * 6!/4!*2! + 4!/3!*1! * 6!/1!*5! + 4!/4! = 90 + 24 +1 = 115. Answer (B)
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A reading list for a certain course consists of 10 books, of which 4 a 02 May 2018, 10:26
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Bunuel
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
Show more

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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