total number of combinations

Question

Write the total number of possible combinations of 5 dice being rolled at once?

Answer 1

Total possible outcome will be  6 ⁵ possible states.

 

   Think of flipping a coin 3 times : 2 state of ( head or tail )  can occur in 2^3= 8 possible way each with

 

     probability of 1/8 as follows:

 

      {HHH , HHT, HTH, HTT, THH, THT,TTH, TTT}:

 

    By the same argument every die with 6 possible outcome out of throwing, when through 5 times it

 

      will have 6^5= 7776 possible outcome .

 

Answer 2

First understand that rolling the 5 dice all at once will not produce a different answer than rolling each of 5 dice one at a time. (They're independent so the 1st roll doesn't affect the 2nd, etc., so rolling all at once is the same.)

 

So think of this as a series of 5 events, each one consisting of the roll of a die.

How many possible outcomes are there for the first roll?  How many possible outcomes from the second roll?  Etc.

 

Then use your multiplication rule to get the answer.

 

This is similar to, say, tossing 3 coins.

You have 2 outcomes on toss 1, you have 2 outcomes for toss 2, and 2 outcomes for toss 3.

 

Hence 2 * 2 * 2 (multiplication rule) = 8 possible overall combinations

 

The dice is the same concept.