Question

(a) We have three standard 6-sided dice, colored red, yellow, and green. In how many ways can we roll them to get a sum of 9? The dice are colored so that a red 2, yellow 3, and green 4 is a different roll from red 3, yellow 4, and green 2.
(b) We have 10 standard 6-sided dice, all different colors. In how many ways can we roll them to get a sum of 20?


PLEASE EXPLAIN THOROUGHLY!

Answer 1

I believe that there are 23 different ways to get a total of 20. Then we need to find the number of ways to get each of the 23 different ways. For instance, one way is 6 6 1-1-1-1- 1-1-1-1: 101 / (21-8) = 45 (different ways to get this result) 10 different dice are rolled, giving the 101 in the numerator since the 6 is used twice, divide by 21, since the 1 is used 8 times, divide by 8! Etc., etc., etc. Final answers, add all these results together. I'm not sure about part B! I'm sorry!!!