Question

You are ordering a hamburger and can get up to 8 toppings, but each topping can only be used once. you tell the cashier to surprise you with the toppings you get. what is the probability that you get 2 toppings? express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

There are 8 toppings.
The probability of getting a particular topping is p = 1/8.
The probability of not getting a particular topping is q = 1-p = 7/8.

Note that ₈C₂ = 28

The probability of getting 2 toppings is
$_{8}C_{2} \,p^{2}q^{6} = \frac{8!}{2!6!} ( \frac{1}{8})^{2}( \frac{7}{8})^{6} = 0.1963$

Answer: 0.1963