Question

In five throws with a single die what is the chance of throwing $\left(1\right)$ three aces exactly, $\left(2\right)$ three aces at least.

Answer 1

Probability of getting ace in single throw $=\frac{1}{6}$

Probability of not getting an ace $=\frac{5}{6}$

Chance of getting exactly three aces in five throws ${=}^5{C}_3{\left(\frac{1}{6}\right)}^3{\left(\frac{5}{6}\right)}^2$

Probability of getting atleast three aces ${=}^5{C}_3{\left(\frac{1}{6}\right)}^3{\left(\frac{5}{6}\right)}^2{+}^5{C}_4{\left(\frac{1}{6}\right)}^4{\left(\frac{5}{6}\right)}^1{+}^5{C}_5{\left(\frac{1}{6}\right)}^5$