1
$\begingroup$

The number of ways of getting three of a kind $(x, x, x, y, z)$ when rolling 5 dice is -

$${5 \choose 3}{2 \choose 1}{6 \choose 1}{5 \choose 2}$$

${5 \choose 3}$ - Ways of choosing dice for the $x$'s

${2 \choose 1}$ - Ways of choosing dice for the $y$

${6 \choose 1}$ - Ways of choosing the number for the $x$'s

${5 \choose 2}$ - Ways of choosing the numbers for the $y$ and $z$

I am looking for the intuition behind why we can't have $6 \choose 3$ for the ways of choosing the numbers for $x, y, z$. I actually know why it is but I could really use a clear intuitive explanation so my head isn't wrecked with it. I want to be able to visualize it quickly and clearly.

  • 0
    You would still need to choose which of your $3$ number is the tri one2012-11-11
  • 0
    I have [a blog article about this](http://blog.plover.com/math/yahtzee.html) that you might find helpful.2012-11-16

1 Answers 1