First time posting a question so assistance is greatly appreciated. I saw a similar question but didn't see the response to item d.) which is what I need to finish a comparable question.
Number of ways to distribute 20 identical pencils to 6 children with no restrictions.
d) If the pencils are given out randomly. What is the probability that there are at least two kids receive the same number of pencils if every kid receives at least one pencil?
Please provide a step-by-step answer on how you got your final answer. I used combinations to arrive to the other answers so that will be helpful. Please let me know if I'm unclear. Thank you all for your assistance. If this was already answered, please provide the link of the post. Thanks!
EDITED: In a similar question, someone wrote... If they all get the different number of pencils, then there would be at least 1+2+3+4+5+6=21 pencils which is impossibile.
So the probability that at least two will get the same number of pencil is 1.
It is impossible that everyone gets a different number of pencils if each gets at least one pencil. So the probability that at least two will get the same number of pencils is 100%.
I understand that yes, two kids will at least receive the same number of pencils but I don't understand the equation if any. I drew it out but can't think of the equation. Would it be C(20,8)?