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31 May 2019, 00:01
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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Question Stats:
67% (02:11) correct
33%
(02:35)
wrong
based on 256
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For her Halloween display, Margaret plans to arrange a row of alternating witch and ghost figurines. The row must begin with a witch figurine and end with a ghost figurine. Margaret plans to purchase either three of each type of figurine or four of each type of figurine, and each figurine will look unique. Depending on how many figurines she purchases, which of the following could be the number of ways that she could arrange her display?
I. 36
II. 72
III. 576
A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
I. 36
II. 72
III. 576
A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
Archit3110
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31 May 2019, 03:59
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Bunuel
4 of each type ; 4!*2 = 576
or 3 of each type ; 3!*2= 36
IMO D
31 May 2019, 07:47
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I don't think it's clear how to answer the question. Since it's possible for her to buy 4 (or maybe more?) figurines of each type, then when she buys only three of each, there are still at least 4 possible options for the first figurine in her display -- any of the 4 (or more) she might have chosen to buy. If there were ten different witch figurines at the shop, she'd have ten choices for her first figurine. The phrase "Depending how many figurines she purchases" alone does not, at least the way I'd interpret it, direct me to a unique interpretation of the question.
I'd guess we're meant to answer the question: how many displays are possible using 3 witches and 3 ghosts, and how many are possible using 4 witches and 4 ghosts? Since we know the 6-figurine display alternates WGWGWG, in that order, then counting our choices for each figurine, we have (3)(3)(2)(2)(1)(1) = 36 possible displays. Similarly with 4 figurines of each type, we have 4! * 4! = 576 possible displays.
I'd guess we're meant to answer the question: how many displays are possible using 3 witches and 3 ghosts, and how many are possible using 4 witches and 4 ghosts? Since we know the 6-figurine display alternates WGWGWG, in that order, then counting our choices for each figurine, we have (3)(3)(2)(2)(1)(1) = 36 possible displays. Similarly with 4 figurines of each type, we have 4! * 4! = 576 possible displays.
