We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

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!

@Melody, if I solve the answer before you do, I will remember to get on here and check your answer! I'm sorry you think I'm rude.

Jeff123 Oct 13, 2017

#1**+1 **

There are 85,228 ways of getting 20 when rolling 10 dice. The probability of rolling a total of 20 is:

85,228 / (6^10) =85,228 / 60,466,176 =0.00140951 x 100=0.140951%.

The calculations for these odds are exactly the same as calculating the coefficient of x^20 in the expansion of this: (x+x^2+x^3+x^4+x^5+x^6)^10. So that x^20 =85,228x^20.

To read about this in detail, see this page of "Mathworld": http://mathworld.wolfram.com/Dice.html

Guest Oct 13, 2017

#2**+1 **

I'm not sure I understand the website. Can you rephrase it so it is simpler?

I found out that we must find how many ways are there to give out 20 dots to 10 dice. Try simplifying that and find a pattern... I'm working on that right now

Jeff123 Oct 13, 2017

#3**+1 **

CPhill can explain it much better than I can. He can show you how to calculate the coefficient of x^20 in the expansion of the above sequence.

Guest Oct 13, 2017

#5**0 **

You still have not responded to my last answer even though I specifically requested you to.

That was 2.5 weeks ago. Why would I bother responding to this new question?

Melody Oct 13, 2017

#6**0 **

Here is your question posted here and the answers. Go through it in detail:

http://web2.0calc.com/questions/counting-question#r17

Guest Oct 13, 2017

#7**0 **

This is the one I was actually referring to:

https://web2.0calc.com/questions/probability-and-geometry#r7

Melody
Oct 13, 2017