I have forgotten my grad school probability and need some help with the following.

I am trying to create a .xls that I can use to look at the odds of multiple dice throws.

Quantity of dice = 10 (n)

# of sides per dice = 20 (s)

Each dice has the following colors instead of numbers:

4 Yellow sides (this could be 1,2,3,4)

3 Blue sides (5,6,7)

2 Green sides (8,9)

1 Red side (10)

1 White side (11)

1 Black side (12)

I would like to understand/know the formula(s) that would help determine the probability of the following different scenarios:

Scenario (each scenario a separate 10 dice roll):

1) Probability of rolling a combination of yellows across the 10 dice, lets say 12 yellow side results

2) Probability of rolling 2 Red sided across the 10 dice - is this 2 times (P(X=r) = nCr * pʳ * (1-p)ⁿ⁻ʳ)?

3) Probability of rolling 3 yellow, 4 blue, 1 green, 0 red, 1 white and 3 black

I have looked at some joint probability examples and have tried to brute force the answer in .xls but I am not quite getting it.

Thank you in advance for any assistance....Steve

I am trying to create a .xls that I can use to look at the odds of multiple dice throws.

Quantity of dice = 10 (n)

# of sides per dice = 20 (s)

Each dice has the following colors instead of numbers:

4 Yellow sides (this could be 1,2,3,4)

3 Blue sides (5,6,7)

2 Green sides (8,9)

1 Red side (10)

1 White side (11)

1 Black side (12)

I would like to understand/know the formula(s) that would help determine the probability of the following different scenarios:

Scenario (each scenario a separate 10 dice roll):

1) Probability of rolling a combination of yellows across the 10 dice, lets say 12 yellow side results

2) Probability of rolling 2 Red sided across the 10 dice - is this 2 times (P(X=r) = nCr * pʳ * (1-p)ⁿ⁻ʳ)?

3) Probability of rolling 3 yellow, 4 blue, 1 green, 0 red, 1 white and 3 black

I have looked at some joint probability examples and have tried to brute force the answer in .xls but I am not quite getting it.

Thank you in advance for any assistance....Steve

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