Ruby McTube has four six sided die.
They each have the following numbers on their six faces:
If she rolls all four, the probability they each show a different number on top is where and are coprime positive integers.
What is ?
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For a given combination (i.e. First die = 1 , Second die = 2 , Third die = 4 , Fourth die = 6 ) the probability of getting this combination is 3 1 × 3 1 × 6 1 × 6 1
And there are 4 ! = 2 4 such combinations.
So, the probability they are all different = 2 4 × 3 1 × 3 1 × 6 1 × 6 1 = 2 7 2
2 + 2 7 = 2 9