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An ordinary 6-sided die has a number on each face from 1 to 6 (each number appears on one face). How many ways can I paint two faces of a die blue, so that the product of the numbers on the painted faces isn't equal to 6?

 

There are 13 ways:

 

Total number of distinct ways to pair two faces

= C(6,2) = 6! / (2!4!) = 15

Total number of ways to pair two faces so that the product equals six

=cardinality {1*6, 2*3} = 2

Therefore

number of ways to paint two faces such that the product is not six

= 15 - 2

=13

 

Is this correct???

 Aug 25, 2021
 #1
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No! I don't think so. There are: [1, 6], [6, 1], [2, 3], [3, 2] ==4 ways of painting the die !.

 Aug 25, 2021
 #3
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Remember, they are using the same dice, so 2,3 is the same as 3,2

SparklingWater2  Aug 25, 2021
 #2
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It seems correct to me

 Aug 25, 2021

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