Question

Four dices (six sided) are thrown one after the other, what is the probability of getting a different number on each dice

Answer 1

Total combinations possible for four dices = 6*6*6*6.

Total combinations of getting a different number on each dice = 6*5*4*3.

So, the required probability = $\frac{6*5*4*3}{6*6*6*6}$ = $\frac{5}{18}$

Answer 2

Find the total number of possible outcomes:

Each dice has 6 faces

Total number of possible outcomes = 6 x 6 x 6 x 6 = 1296

Find the total number of possible outcomes with different number on each dice:

Number of choices 1st dice has = 6

( that is, any of the numbers)

Number of choices 2nd dice has = 5

( that is, any numbers except what is on 1st dice)

Number of choices 3rd dice has = 4

( that is, any numbers except what are on 1st and 2nd dice)

Number of choices 4th dice has = 3

( that is, any numbers except what are on 1st, 2nd and 3rd dice)

Total number of possible outcome = 6 x 5 x 4 x 3 = 360

Find the probability :

P(Different number on each dice) = 360/1296 = 5/18

Answer: The probability is 5/18