How can I calculate the probability of X = 1,2,3 in a three-toss die experiment?

[leptons]

Consider the experiment of tossing a die thrice. X is defined as the number of different faces that appear (i.e., X = 1,2,3). What is meant by the "number of different faces that appear"? Could you help me how could I get P(X = 1,2,3)?

 

[TenaliRaman]

well,
u r rolling three dice ... so u could get them all different so number of different faces u will have is 3 ... or you could get 2 same numbers but 1 different , so number of different faces u see is 2 ... or u could get all the three numbers same which means number of different faces u see is 1.

so X can take values 1,2 and 3.

Now u can solve it pretty easily in two possible ways ,
1> enumerate all possible triplets
(1,1,1),(1,1,2),...(6,6,6).
then simply do the counting.

2> if you are good at combinatorics ... then u can do it faster by considering
a. number of ways u can get all three numbers different
b. number of ways u can get two numbers same and 1 different
c. number of ways u can get all three numbers same

-- AI