Three dices D1,D2,D3 are thrown. Find the probability that two numbers of two dices matches only.

When the three dice are thrown,the total possibilities are 6×6×6=216
We have to find the probability that two numbers of two dice match :

1)The number of cases in which all the three dice give the same number are:(1,1,1),(2,2,2),(3,3,3),(4,4,4),(5,5,5),(6,6,6)=6 cases
2)The number of cases in which all dice give different numbers=6×5×4=120  
(This is because when the first die is thrown,any 6 numbers are  but when the second die is thrown 5 possible number are there because in this case the second die cant show the same number as the first die and similarly fir the third die 4 numbers are possible)
3)So the cases in which two die match=Total cases-cases in which all die show same number-cases in which all die show different numbers=216-120-6=90

SO the required probability=90216=512 

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