+4 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???
No! I don't think so. There are: [1, 6], [6, 1], [2, 3], [3, 2] ==4 ways of painting the die !.
+591 Remember, they are using the same dice, so 2,3 is the same as 3,2
