Three different dice are rolled at three different times. The probability that they will show different numbers only two times?

Dear Student,

Please find below the solution to the asked query:

We know formula for probability :

Probability P ( E )  = $\frac{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{desired} \mathrm{events} \mathrm{n} ( \mathrm{E} )}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{events} \mathrm{n} ( \mathrm{S} )}$

Here , We throw three dice and get :

So,

n ( S ) = 216

And

Show different numbers only two times (  Marked in red box )

n ( E ) = 90

Therefore ,

Probability of  getting different numbers only two times = $\frac{90}{216} =\mathbf{ }\frac{\mathbf{5}}{\mathbf{12}}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)}$

Hope this information will clear your doubts about Probability .

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