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by bharti.2010 » Sun Jan 08, 2012 3:10 pm
Ques: 3 marbles are placed at each corner of a traingle. 2 arrangements of the marbles are considered different only if the relative position of the marbles are different. How many different ways are there to arrange the 3 marbles?

1. 1
2. 2
3. 3
4. 4
5. 6
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by pemdas » Sun Jan 08, 2012 4:05 pm
relative position is considered with the permuted (ordered) sets
3P2=3!=6
edit: 3P2/3=2
bharti.2010 wrote:Ques: 3 marbles are placed at each corner of a traingle. 2 arrangements of the marbles are considered different only if the relative position of the marbles are different. How many different ways are there to arrange the 3 marbles?

1. 1
2. 2
3. 3
4. 4
5. 6
Last edited by pemdas on Mon Jan 09, 2012 7:17 am, edited 1 time in total.
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by santhoshsram » Sun Jan 08, 2012 4:53 pm
IMO B

This is similar to arranging 3 marbles in a circle (the circle would be the circle that circumscribes the triangle).

Also, 2 arrangements are different only if the relative positions of the marble are different. So one marble's position is fixed. Total number of arrangements = number of arrangements of the remaining two marbles [spoiler]= 2! = 2. Or the formula for computing the number of ways of arranging n object in a circle = (n-1)! i.e. (3-1)! = 2 [/spoiler].

If we consider A, B, C as the 3 marbles, the only two unique arrangements are ABC and ACB. Each of the other 4 arrangements can be obtained by rotating one of these two triangles.
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by bharti.2010 » Sun Jan 08, 2012 5:15 pm
Yes Santosh you are correct. Answer is 2.
I got confused in the statement which says " relative position of the marbles are different".
Thanks for your explanatio.
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by ronnie1985 » Mon Jan 09, 2012 2:21 am
There are only 2 ways as one marble top be treated fixed. The other two can be arranged in 2!Q ways = 2 ways.
(B) is answer.
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by pemdas » Mon Jan 09, 2012 7:16 am
yes Santosh, i missed that it's circular permutation
therefore, 3P2/3=2
choice b
santhoshsram wrote:IMO B

This is similar to arranging 3 marbles in a circle (the circle would be the circle that circumscribes the triangle).

Also, 2 arrangements are different only if the relative positions of the marble are different. So one marble's position is fixed. Total number of arrangements = number of arrangements of the remaining two marbles [spoiler]= 2! = 2. Or the formula for computing the number of ways of arranging n object in a circle = (n-1)! i.e. (3-1)! = 2 [/spoiler].

If we consider A, B, C as the 3 marbles, the only two unique arrangements are ABC and ACB. Each of the other 4 arrangements can be obtained by rotating one of these two triangles.
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by force5 » Mon Jan 09, 2012 9:12 am
yes got it right this time. (3-1)! -- relative positions is the key
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