# Calculate probabilities. 40 sixes out of a 100 fair die rolls & 20 sixes out of a 100 fair die roll

I tried to calculate using the formula from an older question on here but it keeps telling me there's an error.

I used $\frac{100\times60}{40}\times\frac1{6^{40}} \times (1-1/6)^{100-40}$.

• Why don't you include (in your post) the formula you tried using? Nov 30, 2013 at 16:10

If the probability to one event is $p$, the probability to k events out of n is: $$P={n \choose k}p^k(1-p)^{n-k}$$
The probability for one six in die roll is $\frac16$. So, according to the formula, the probability for $40$ sixes out of $100$ rolls is: $$P={100 \choose 40}{\left(\frac16\right)}^{40}{\left(\frac56\right)}^{60}$$
the probability for $20$ sixes out of $100$ rolls is: $$P={100 \choose 20}{\left(\frac16\right)}^{20}{\left(\frac56\right)}^{80}$$