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A reading list for a certain course consists of 10 books, of which 4 a

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A reading list for a certain course consists of 10 books, of which 4 a  [#permalink]

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New post 13 May 2015, 02:53
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Question Stats:

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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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Re: A reading list for a certain course consists of 10 books, of which 4 a  [#permalink]

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New post 13 May 2015, 04:00
1
1
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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Re: A reading list for a certain course consists of 10 books, of which 4 a  [#permalink]

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New post 13 May 2015, 06:25
3
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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Re: A reading list for a certain course consists of 10 books, of which 4 a  [#permalink]

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New post 13 May 2015, 10:18
1
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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Re: A reading list for a certain course consists of 10 books, of which 4 a  [#permalink]

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New post 14 May 2015, 05:12
1
Bunuel wrote:
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

Kudos for a correct solution.



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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Re: A reading list for a certain course consists of 10 books, of which 4 a  [#permalink]

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New post 15 May 2015, 01:23
Bunuel wrote:
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
[/i]


Ans: B

Solution: Selection requires at most 2 novels, means=
0N & 4P + 1N & 3P + 2N & 2P
6c0*4c4+ 6c1*4c3 + 6c2*4c2
= 1+ 24 + 90
= 115

Ans: B
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Re: A reading list for a certain course consists of 10 books, of which 4 a  [#permalink]

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New post 15 May 2015, 08:49
1
Bunuel wrote:
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

Kudos for a correct solution.


Required selection=(4C2*6C2)+(6C1*4C3)+(4C4)
=90+24+1
=115
Answer B
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Re: A reading list for a certain course consists of 10 books, of which 4 a  [#permalink]

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New post 15 May 2015, 16:29
the answer is B 115

including at most 2 novels means that no novels included or one novels included or 2 novels included

no novels included =4C4= 1

one novels included = 4C3*6C1=24

2 novels included = 4C2*6C2=90

selections of 4 books satisfy the requirements= 1+24+90=115
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A reading list for a certain course consists of 10 books, of which 4 a  [#permalink]

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New post 18 May 2015, 06:41
Bunuel wrote:
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

Kudos for a correct solution.


OFFICIAL SOLUTION:

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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A reading list for a certain course consists of 10 books, of which 4 a  [#permalink]

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New post 31 May 2017, 18:02
Bunuel wrote:
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


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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Re: A reading list for a certain course consists of 10 books, of which 4 a  [#permalink]

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