Relative Likelihood of n Sixes on 6n Dice/Mistake

Source Work

 * The Puzzles:
 * Prince Rupert's Cube
 * $129$ (Solution)
 * $129$ (Solution)

Mistake

 * Our short table shows the probabilities, rounded to three decimals, of obtaining the mean number or more sixes when $6 n$ dice are tossed.


 * {| border="1"

! align="right" style = "padding: 2px 10px" | $6 n$ ! align="right" style = "padding: 2px 10px" | $n$ ! style = "padding: 2px 10px" | $\map P {\text {$n$ or more sixes} }$
 * align="right" style = "padding: 2px 10px" | $6$
 * align="right" style = "padding: 2px 10px" | $1$
 * align="right" style = "padding: 2px 10px" | $0.665$
 * align="right" style = "padding: 2px 10px" | $12$
 * align="right" style = "padding: 2px 10px" | $2$
 * align="right" style = "padding: 2px 10px" | $0.619$
 * align="right" style = "padding: 2px 10px" | $18$
 * align="right" style = "padding: 2px 10px" | $3$
 * align="right" style = "padding: 2px 10px" | $0.597$
 * align="right" style = "padding: 2px 10px" | $24$
 * align="right" style = "padding: 2px 10px" | $2$
 * align="right" style = "padding: 2px 10px" | $0.584$
 * align="right" style = "padding: 2px 10px" | $30$
 * align="right" style = "padding: 2px 10px" | $5$
 * align="right" style = "padding: 2px 10px" | $0.576$
 * align="right" style = "padding: 2px 10px" | $96$
 * align="right" style = "padding: 2px 10px" | $6$
 * align="right" style = "padding: 2px 10px" | $0.542$
 * align="right" style = "padding: 2px 10px" | $600$
 * align="right" style = "padding: 2px 10px" | $100$
 * align="right" style = "padding: 2px 10px" | $0.517$
 * align="right" style = "padding: 2px 10px" | $900$
 * align="right" style = "padding: 2px 10px" | $150$
 * align="right" style = "padding: 2px 10px" | $0.514$
 * }
 * align="right" style = "padding: 2px 10px" | $600$
 * align="right" style = "padding: 2px 10px" | $100$
 * align="right" style = "padding: 2px 10px" | $0.517$
 * align="right" style = "padding: 2px 10px" | $900$
 * align="right" style = "padding: 2px 10px" | $150$
 * align="right" style = "padding: 2px 10px" | $0.514$
 * }
 * }

Correction
The $6$th line is incorrect.

For $96$ dice, you are looking to score at least $16$ sixes, not $6$, as $\dfrac {96} 6 = 16$ not $6$.