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For her Halloween display, Margaret plans to arrange a row

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sandy

Retired Moderator

Joined: 07 Jun 2014

Posts: 4805

GRE 1: Q167 V156

WE:Business Development (Energy and Utilities)

For her Halloween display, Margaret plans to arrange a row [#permalink]

Updated on: 08 Jan 2018, 16:35

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38% (02:31) wrong

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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?

Indicate all possible values.

A. 6
B. 24
C. 36
D. 72
E. 576
F. 720
G. 40,320

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Originally posted by sandy on 30 Dec 2017, 14:06.
Last edited by sandy on 08 Jan 2018, 16:35, edited 1 time in total.

sandy

Retired Moderator

Joined: 07 Jun 2014

Posts: 4805

GRE 1: Q167 V156

WE:Business Development (Energy and Utilities)

Re: For her Halloween display, Margaret plans to arrange a row [#permalink]

08 Jan 2018, 16:34

Expert Reply

Explanation

This problem is about permutations, because the order of the figurines matter since they each look unique.

You have two cases to consider here. Start with the option that Margaret buys three witches and three ghosts. In that case, she has 3 choices of witch for the first spot, 3
choices of ghost for the second spot, 2 choices of witch for the third spot, 2 choices of ghost for the fourth spot, 1 choice of witch for the fifth spot, and 1 choice of ghost for the sixth spot:

Hence, her total number of arrangements is 3 × 3 × 2 × 2 × 1 × 1 = 36, which is choice (C). If she buys four of each figurine, her number of arrangements is 4 × 4 × 3 × 3 × 2 × 2 × 1 × 1 = 576, choice E.

Hence options C and E are correct!
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yell2012prime

Intern

Joined: 20 Dec 2017

Posts: 30

Re: For her Halloween display, Margaret plans to arrange a row [#permalink]

15 Jan 2018, 06:33

3!*3!=36
4!*4!=576
ans C & E

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Re: For her Halloween display, Margaret plans to arrange a row [#permalink]

28 Sep 2021, 10:29

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