A pizza shop offers nin toppings. No topping is used more than once. What is the probability that the toppings are pepperoni, onions, olives, and mushrooms? Round your answer to the nearest thousandth.
Excel spreadsheets are very helpful for these kinds of problems.
There are 9-choose-0 ways =1 to have a pizza with zero toppings.
9-choose-1 ways = 9 to have 1 topping
9-choose-2 = 36 ways to have 2 toppings
9-choose-3 = 84 ways to have 3 toppings
Repeat for all 4 through 9 toppings.
Then sum all your answers. This is the denominator. The numerator is one.
To find the probability, we need to know the total number of possible combinations of toppings and the number of combinations that include pepperoni, onions, olives, and mushrooms.
Since there are nine toppings, we have nine choices for the first topping, eight choices for the second topping, seven choices for the third topping, and six choices for the fourth topping.
The total number of possible combinations is the product of these choices: 9 x 8 x 7 x 6 = 3,024.
Now, we need to determine the number of combinations that include pepperoni, onions, olives, and mushrooms. Since each topping can only be used once and we have four specific toppings, there is only one possible combination that includes all four toppings.
Therefore, the number of combinations that include pepperoni, onions, olives, and mushrooms is 1.
Now, we can calculate the probability by dividing the number of successful outcomes (1) by the total number of possible outcomes (3,024).
Probability = 1 / 3,024 ≈ 0.00033 (rounded to the nearest thousandth)
So, the probability that the toppings are pepperoni, onions, olives, and mushrooms is approximately 0.00033.