Question

Six dices are thrown simultaneously find the probability that all dices show different faces

Answer 1

Total number of possible combinations (size of sample space) when six dice are thrown are 6^6 = 46656

The general formula for size of sample space = 6^(number of dice)

Now, you want to find the possible ways in which 6 dice show different faces.

This problem reduces to permutations of arranging all the faces 1,2,3,4,5,6 on 6 dice

First die can choose from 6 choices.

Second die can choose from 5 remaining choices leaving the face chosen by first die.

Third die is left with 4 choices, fourth with 3, fifth with 2, and last with 1.

Thus, total combinations = 6*5*4*3*2*1 = 6! = 720

Thus, probability = 720/46656