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Math Help - trinomal distribution dice problem

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    Question trinomal distribution dice problem

    Three fair dice are rolled simultaneously. In 10 independent throws,

    let X: number of times all the dice show same face

    let Y: number of times exactly 2 dice show same face

    let p_1,p_2,p_3 be corresponding probabilities of
    X, Y, Z=n-X-Y

    pdf of trinomial distribution,

    p(X=3, Y=3)= 10C3* (10-3)C3* p_1^3* p_2^3* p_3^4
    i understand p_1= 6/6^3

    but what are the values of p_2,p_3 ?
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    Quote Originally Posted by amul28 View Post
    Three fair dice are rolled simultaneously. In 10 independent throws,

    let X: number of times all the dice show same face

    let Y: number of times exactly 2 dice show same face

    let p_1,p_2,p_3 be corresponding probabilities of
    X, Y, Z=n-X-Y

    pdf of trinomial distribution,

    p(X=3, Y=3)= 10C3* (10-3)C3* p_1^3* p_2^3* p_3^4
    i understand p_1= 6/6^3

    but what are the values of p_2,p_3 ?
    How many ways can exactly two dice show the same face? Divide that number by 6^3.

    p3 = 1 - (p1 + p2).
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