In order to decide who will play first in a certain board game, each player rolls a four-sided die; the player with the highest score begins.Three people  decide to play the game. What is the...

In order to decide who will play first in a certain board game, each player

rolls a four-sided die; the player with the highest score begins.Three people 

decide to play the game. What is the probability that when they roll the die

to decide who starts, they all obtain different scores?

 

 

 

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In order to decide who will play first in a certain board game, each player rolls a four-sided die; the player with the highest score begins. Three people decide to play the game.

Each player can get 4 numbers when the die is rolled. The total number of ways in which they can roll their dice is 4*4*4 = 64 The number of ways in which they can roll their dice and obtain different numbers is 4*3*2 = 24. This gives the probability of the given event happening as `24/64 = 3/8`

The probability that when they roll the dice to decide who starts, they all obtain different scores is `3/8`

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