3 dice are thrown simultaneously ,find the probability that -
(1) all of them show the same face.
(2) all shows distinct faces.
(3) two of them show the same face.

Dear Student,
Please find below the solution to the asked query:

1As there are 6 faces on dice, henceProbabilty of getting a face on dice=16So we want to have same face Any one of the 6 faces on three dice.Required Probabilty=6C1 16×16×16=66×6×6=136 Answer2 As now we want three distinct numbers, first dice has 6 choices, second dicehas 5 choices while third dice has 4 choices.Required Probabilty=6×5×46×6×6=59 Answer3 First we chooces two dice from three dice. Then we we will choose 1 numberfrom 6 numbers which we can to see on two dice, then we will choose, 1 numberfrom remaining 5 numbers for third dice.Required Probabilty= 3C2×6C1×5C16×6×6= 3C1×6C1×5C16×6×6= 3×6×56×6×6=512 Answer

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