A Student Is Given a Reading List of Ten Books for Which He Must Select Two
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A reading list for a certain class consists of ten books, of which 4 a [#permalink] 
13 May 2015, 02:53
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A reading list for a certain course consists of ten books, of which iv 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
East. 195
Kudos for a right solution.
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Re: A reading list for a sure course consists of 10 books, of which 4 a [#permalink] 13 May 2015, 04:00
Can be selected as
Case 1 PPNN 2 Poems out of 4 and 2 Novels out of 6 i.e. 4C2 * 6C2 = xc
or
Instance 2 PPPN iii Poems out of four and 1 Novels out of 6 i.e 4C3 * 6C1 = 24
or
Example 3 PPPP 4 Poems out of 4 i.e. 4C4 =one
Full no. of selections example 1 + case 2+ case three = 90 + 24 +1 = 115
So respond must exist B. 115
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Re: A reading listing for a certain course consists of ten books, of which 4 a [#permalink] 13 May 2015, 06:25
Possibilities include
1novel, 3 poems
6! / 1!5! × 4! /3! 1! =24
2 novels, 3 poems
half dozen!/2! 4! × four!/2! 2! =90
0 novels, 4 poems
=1
24+90+1=115
B. 115
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Re: A reading list for a sure course consists of ten books, of which 4 a [#permalink] thirteen May 2015, 10:18
Novel=N,Poem book=P; therefore ten=4+Novels =>North=six;P=4
The concluding selection would exist = 2N and 2P +1N and 3P + 4P =6C2*4C2 + 6C1*4C3 + 4C4 = xc+24+ane=115
Hence reply is B
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Re: A reading list for a certain course consists of 10 books, of which 4 a [#permalink] 14 May 2015, 05:12
Bunuel wrote:
A reading listing for a certain form consists of 10 books, of which 4 are poems and the rest are novels. Each student is required to read a selection of iv books from the list, including at most 2 novels. How many selections of 4 books satisfy the requirements?
A. xc
B. 115
C. 130
D. 144
E. 195
Kudos for a correct solution.
Options with ii novels: 6C2 * 4C2 = 90
Options with one novel: 4C3 * 6C1 = 24
Option with no novel: 4C4 = i
so 90+24+one = 115
Answer is B
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Re: A reading list for a certain course consists of x books, of which 4 a [#permalink] 15 May 2015, 01:23
Bunuel wrote:
A reading list for a certain course consists of ten books, of which four are poems and the residuum are novels. Each educatee is required to read a selection of iv books from the listing, including at almost ii novels. How many selections of 4 books satisfy the requirements?
A. 90
B. 115
C. 130
D. 144
Eastward. 195
[/i]
Ans: B
Solution: Pick requires at almost 2 novels, ways=
0N & 4P + 1N & 3P + 2N & 2P
6c0*4c4+ 6c1*4c3 + 6c2*4c2
= one+ 24 + 90
= 115
Ans: B
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Re: A reading list for a certain class consists of 10 books, of which iv a [#permalink] 15 May 2015, 08:49
Bunuel wrote:
A reading listing for a certain class consists of 10 books, of which 4 are poems and the residual are novels. Each educatee is required to read a selection of 4 books from the list, including at nearly two 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 choice=(4C2*6C2)+(6C1*4C3)+(4C4)
=90+24+1
=115
Reply B
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Re: A reading list for a certain course consists of ten books, of which 4 a [#permalink] 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
i novels included = 4C3*6C1=24
2 novels included = 4C2*6C2=ninety
selections of iv books satisfy the requirements= 1+24+90=115
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A reading list for a certain form consists of 10 books, of which four a [#permalink] 18 May 2015, 06:41
Bunuel wrote:
A reading list for a certain course consists of ten books, of which iv are poems and the residual are novels. Each educatee is required to read a option of 4 books from the list, including at most ii novels. How many selections of 4 books satisfy the requirements?
A. ninety
B. 115
C. 130
D. 144
E. 195
Kudos for a correct solution.
OFFICIAL SOLUTION:
Total - restriction =
= (4 books out of x) - ((3 novels and i poem) + (4 novels and 0 poems)) =
\(= C^4_{10} - (C^3_6*C^1_4 + C^4_6) =\)
= 210 - (20*4 + xv) = 115.
Respond: B.
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Re: A reading list for a sure form consists of 10 books, of which 4 a [#permalink] 31 May 2017, 18:02
Bunuel wrote:
A reading list for a certain course consists of ten books, of which iv are poems and the residuum are novels. Each student is required to read a selection of iv books from the list, including at most ii novels. How many selections of 4 books satisfy the requirements?
A. ninety
B. 115
C. 130
D. 144
E. 195
We are given that a form reading list contains four poems and 6 novels. Nosotros demand to determine the number of ways a student can select 4 books if at most 2 novels can exist selected.
Scenario one: 4 poems are selected.
4 poems tin be selected in 4C4 = 1 fashion.
Scenario 2: ane novel and 3 poems are selected.
three poems tin can be selected in 4C3 = 4!/[3!(4-3)!] = (four x 3 ten two)/3! = 4 means, and 1 novel tin be selected in 6C1 = vi ways.
Thus, iii poems and ane novel can be selected in four x half-dozen = 24 ways.
Scenario three: two novels and two poems are selected.
2 poems can be selected in 4C2 = 4!/[ii!(4-2)!] = (4 x 3)/2! = vi ways, and 2 novels tin be selected in 6C2 = six!/[two!(vi-ii)!] = (6 x five)/2! = 15 ways.
Thus, 2 poems and 2 novels tin be selected in 6 x 15 = 90 means.
All 4 books with at almost 2 novels tin be selected in 1 + 24 + 90 = 115 ways.
Answer: B
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Re: A reading listing for a certain course consists of 10 books, of which 4 a [#permalink] x Oct 2020, 09:23
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Re: A reading listing for a certain course consists of 10 books, of which iv a [#permalink]
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