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# Alice received a bracelet with four distinct removable charms. How man

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Joined: 02 Sep 2009
Posts: 58340
Alice received a bracelet with four distinct removable charms. How man  [#permalink]

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11 Feb 2019, 02:48
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Difficulty:

5% (low)

Question Stats:

90% (00:29) correct 10% (00:33) wrong based on 60 sessions

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Alice received a bracelet with four distinct removable charms. How many different ways can she arrange the four charms on her new bracelet?

(A) 4
(B) 8
(C) 24
(D) 100
(E) 40,320

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Re: Alice received a bracelet with four distinct removable charms. How man  [#permalink]

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11 Feb 2019, 03:10
Bunuel wrote:
Alice received a bracelet with four distinct removable charms. How many different ways can she arrange the four charms on her new bracelet?

(A) 4
(B) 8
(C) 24
(D) 100
(E) 40,320

4 charms
can be arranged in

4*3*2 *1 = 24 ways
IMO C
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Re: Alice received a bracelet with four distinct removable charms. How man  [#permalink]

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12 Feb 2019, 03:08
Bunuel wrote:
Alice received a bracelet with four distinct removable charms. How many different ways can she arrange the four charms on her new bracelet?

(A) 4
(B) 8
(C) 24
(D) 100
(E) 40,320

Isnt the arrangement in a circle (n-1)!
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Re: Alice received a bracelet with four distinct removable charms. How man  [#permalink]

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13 Feb 2019, 19:44
Bunuel wrote:
Alice received a bracelet with four distinct removable charms. How many different ways can she arrange the four charms on her new bracelet?

(A) 4
(B) 8
(C) 24
(D) 100
(E) 40,320

4 charms can be arranged in 4! = 24 ways.

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Re: Alice received a bracelet with four distinct removable charms. How man  [#permalink]

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29 Apr 2019, 04:32
Bunuel wrote:
Alice received a bracelet with four distinct removable charms. How many different ways can she arrange the four charms on her new bracelet?

(A) 4
(B) 8
(C) 24
(D) 100
(E) 40,320

This is a combinatorics problem:

To figure out all possible ways to arrange given objects, find out its factorial. Here,
Simply take 4!

= 24
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Re: Alice received a bracelet with four distinct removable charms. How man  [#permalink]

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29 Apr 2019, 05:05
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I think you could justify at least three different answers to this question, the way it's worded. Obviously you can arrange four things in 4! = 24 orders, but we're arranging charms in a bracelet. A bracelet is circular, so if our charms are A, B, C and D, then is the arrangement ABCD really any different from BCDA if we can just rotate the bracelet so the second arrangement matches the first? It should be a circular permutation question, not an ordinary one. If we must use all four of the charms, then the answer is simply 3! = 6 (because in a circular arrangement, it doesn't matter where you put the first thing - it's only the arrangement of the rest of the things relative to the first one that matters).

But if that's the correct interpretation of the question, then why does the question say the charms are 'removable'? I'd guess we're also supposed to count the arrangements we could make using only 3 of the charms, or 2 of them, or 1 of them. And if that's the question (and if we need to use at least 1 charm, which also isn't clear from the wording of the question), the answer is 24, but purely by coincidence:

Using all 4 charms: we can make 3! circular permutations, or 6 arrangements
Using only 3 charms: we have 4 choices for which charm to omit, then can make 2! circular permutations, so 8 arrangements
Using only 2 charms: we have 4C2 = 6 choices for which charms to use, then can make 1! = 1 circular permutation, so 6 arrangements
Using only 1 charm: we have 4 choices of which charm to use

and the answer is 6+8+6+4 = 24.

It's not at all clear what the question even means, but I'm sure it wasn't intended to be a straightforward permutation question - if that was the intention, it would just ask how many ways we can line up four objects.
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Re: Alice received a bracelet with four distinct removable charms. How man   [#permalink] 29 Apr 2019, 05:05
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