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A bibliophile plans to put a total of seven books on her mar

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A bibliophile plans to put a total of seven books on her mar [#permalink] New post 05 Oct 2017, 20:39
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A bibliophile plans to put a total of seven books on her marble shelf. She can choose these seven books from a mixture of works from Antiquity and works on Post-modernism, of which there are seven each. If the shelf must contain at least four works from Antiquity, and one on Post-Modernism, then how many ways can he select seven books to go on the shelf?

(A) 441
(B) 1225
(C) 1666
(D) 1715
(E) 1820

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[Reveal] Spoiler: OA
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Re: A bibliophile plans to put a total of seven books on her mar [#permalink] New post 05 Oct 2017, 22:40
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Bunuel wrote:
A bibliophile plans to put a total of seven books on her marble shelf. She can choose these seven books from a mixture of works from Antiquity and works on Post-modernism, of which there are seven each. If the shelf must contain at least four works from Antiquity, and one on Post-Modernism, then how many ways can he select seven books to go on the shelf?

(A) 441
(B) 1225
(C) 1666
(D) 1715
(E) 1820

Kudos for correct solution.


We have three option for these - (we have 7 Antiquity and 7 Post-Modernism)

1. 7C4 * 7C3 = 49 (since we should have at least 4 Antiquity)

2. 7C5 * 7C2 = 441

3. 7C6 * 7C1 = 1225 (since we should have at least 1 Post-Modernism)

Adding these = 49 + 441 + 1225 = 1715 ways
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Re: A bibliophile plans to put a total of seven books on her mar [#permalink] New post 22 Nov 2018, 00:41
pranab01 wrote:
Bunuel wrote:
A bibliophile plans to put a total of seven books on her marble shelf. She can choose these seven books from a mixture of works from Antiquity and works on Post-modernism, of which there are seven each. If the shelf must contain at least four works from Antiquity, and one on Post-Modernism, then how many ways can he select seven books to go on the shelf?

(A) 441
(B) 1225
(C) 1666
(D) 1715
(E) 1820

Kudos for correct solution.


We have three option for these - (we have 7 Antiquity and 7 Post-Modernism)

1. 7C4 * 7C3 = 49 (since we should have at least 4 Antiquity)

2. 7C5 * 7C2 = 441

3. 7C6 * 7C1 = 1225 (since we should have at least 1 Post-Modernism)

Adding these = 49 + 441 + 1225 = 1715 ways


Points 3 & 2 have been interchanged!
Re: A bibliophile plans to put a total of seven books on her mar   [#permalink] 22 Nov 2018, 00:41
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A bibliophile plans to put a total of seven books on her mar

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