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# A certain stationary store arranges notebooks on display such that eac

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Math Expert
Joined: 02 Sep 2009
Posts: 62380
A certain stationary store arranges notebooks on display such that eac  [#permalink]

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07 Feb 2020, 06:46
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Difficulty:

45% (medium)

Question Stats:

66% (01:36) correct 34% (02:00) wrong based on 37 sessions

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A certain stationary store arranges notebooks on display such that each of the seven different colors of notebooks white,yellow, orange, green, red, blue, and purple are consecutive in a repeating pattern. If eight consecutively displayed notebooks are purchased, what is the probability that two of the notebooks are purple?

(A) 1/49
(B) 1/8
(C) 1/7
(D) 2/7
(E) 1/2

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Joined: 07 May 2019
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Location: India
Re: A certain stationary store arranges notebooks on display such that eac  [#permalink]

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08 Feb 2020, 23:44
Bunuel wrote:
A certain stationary store arranges notebooks on display such that each of the seven different colors of notebooks white,yellow, orange, green, red, blue, and purple are consecutive in a repeating pattern. If eight consecutively displayed notebooks are purchased, what is the probability that two of the notebooks are purple?

(A) 1/49
(B) 1/8
(C) 1/7
(D) 2/7
(E) 1/2

Solution:
• There is a total of $$7$$ different colors.
o They are arranged in a consecutive repeating pattern.
 The color of every 8th notebook is the same.
• Now, 8 consecutive notebooks are selected.
o This means there are exactly two notebooks of the same color. (For example, PWTOGRBP)
o There are seven different possibilities for selecting two notebooks of the same color. (Total cases)
• If the first notebook is purple, then the last notebook will also be purple, this is the only favorable case.
o Probability of selecting two purple notebooks = $$\frac{1}{7}$$
Hence, the correct answer is Option C.
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Re: A certain stationary store arranges notebooks on display such that eac   [#permalink] 08 Feb 2020, 23:44
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