Take a Chance with my Photos!

Probability Level 3

I was on a tour of three countries India, France and U.K.

In each country I took photographs of exactly two monuments---

1) In India -- The Taj Mahal and The Golden Temple

2)In France --- The Eiffel tower and The Louvre

3) In U.K. --- The Stonehenge and The London Eye

I shuffled and arranged these 6 photographs at random in a Circle.

What is the percentage probability that the Taj Mahal and the Golden Temple photos are adjacent to each other?


The answer is 40.

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Satyen Nabar by Satyen Nabar , 48, India

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4 solutions

Satyen Nabar
May 22, 2014

n objects can be arranged in a circle in (n-1)!

So 6 objects ABCDEF in 5! = 120 ways.

(AB)CDEF can be arranged in 4! ways = 24. Multiply this by 2! because it can be AB or BA. so 48 ways .

48:120 = 0.4 = 40 %

16 Helpful 0 Interesting 1 Brilliant 0 Confused

Neater solution WOLOG, A can be anywhere on the circle, B can be on two of five places on the circle, 40%

Benjamin Wong - 7 years ago

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This is also what I did! Haha. But I am not sure if this is considered as combinatorics. Hahaha.

Angelo Marco Ramoso - 7 years ago

Definitely a simpler solution. Did not come to my mind....

Nishant Sharma - 7 years ago

Being the Taj Mahal in any place, there are 5 places more, and two of them are adjacent to the Taj Mahal photo. 2/5=0.4=40%

3 Helpful 0 Interesting 0 Brilliant 0 Confused

The total number of photo arrangement:

N = 6 ! = 720 N = 6! = 720

Now stick the photos of the Taj Mahal and the Golden Temple to make sure the two photos are adjacent to each other and shuffle and lay the photos in a straight line instead of putting in a circle. In this case, there are 5! permutations but for each permutation, there are 2 ways to arrange the adjacent photos, therefore, there are:

M 1 = 2 × 5 ! = 240 M_1 = 2\times 5! = 240

But M1 does not include the cases where the two Indian photos are at the edge. Fix the two photos and shuffle, there are 4! permutations and for each permutation there are 2 ways of fixing the 2 photos at the edges.

M 2 = 2 × 4 ! = 48 M_2 = 2\times 4! = 48

The total number of arrangements where the two Indian photos are adjacent are:

M = M 1 + M 2 = 240 + 48 = 288 M = M_1 + M_2 = 240 + 48 = 288

The probability is:

p = M N = 288 720 = 0.4 p = \frac{M}{N} = \frac{288}{720} = 0.4

The probability p = 40%

2 Helpful 0 Interesting 0 Brilliant 0 Confused

6 photos can be arranged in a circle in (6-1)! ways i.e 120 ways Let treat two photos from India as a single photo .hence total no of arrangement is (5-1)!2!=48 Probability is 48÷120=0.4 % of probability is 0.4×100=40%

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Thats what i did.... the idea of combinations and permutations is good

rishabh singhal - 7 years ago

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