SOLUTION: a die is loaded in such a way that the probabilityof the face with j dots turning up is proportional to j for j=1,2,3,4,5,6. in 6 independent throws of this die , what is the proba

Question 252101: a die is loaded in such a way that the probabilityof the face with j dots turning up is proportional to j for j=1,2,3,4,5,6. in 6 independent throws of this die , what is the probability that each face turns up exactly one?
Answer by vksarvepalli(154) (Show Source): You can put this solution on YOUR website!
let the probability of face with 1 dot turning up be 1k
the probability of face with 2 dots turning up 2k
the probability of face with 3 dots turning up 3k
and so on
but since an outcome should be any one the face the sum of all these should be 1
so,1k+2k+3k+4k+5k+6k=1
that is 21k=1
we get k= 1/21
now the probability that each face turns up exactly once in 6 throws is
1k*2k*3k*4k*5k*6k
that is
so the answer is or Factorial 6/21^6
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