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Minorities stick together

Consider the following scenario.

How many ways can you arrange the shoes, so that the black shoes must always be together?

Before we tackle this problem, let’s simplify it a little. Let’s imagine they are all in a straight line. B = black shoes, T = tri-coloured shoes. Let’s try to see all the possibilities.

B B T T T T =   5  x  4  x  3  x  2  x  1  x  2  =  240

Therefore, the total number of possibilities are 240.

Now, back to the scenario.

If we arrange the shoes in a circle, will the answer be the same?

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August 27, 2010 Posted by | Additional Mathematics Form 5 | Leave a comment