Question

You are ordering a hamburger and can get up to 7 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 3 toppings? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

According to the given question, one can get up to 7 toppings, but each topping can only be used once when we are ordering a hamburger . Therefore, the chance of getting any topping are as

Therefore the probability that we get 3 toppings is determined as:

(to get 3 toppings)

$=\frac{^{7}C_{3}}{^{7}C_{0}+^{7}C_{1}+^{7}C_{2}+^{7}C_{3}+^{7}C_{4}+^{7}C_{5}+^{7}C_{6}+^{7}C_{7}}$

$=\frac{35}{1+7+21+35+35+21+7+1}$

$=\frac{35}{128}$

$=0.2734$

(rounded to four decimal places)