A pizza place sells five topping pizzas with the following options. Crust: Classic, Crispy Toppings: Extra cheese, pepperoni, sausage, onions, banana peppers, jalapenos, tomatoes, fresh herbs, mushrooms, black olives.

What is the probability that a customer will order a five topping pizza including onions, jalapenos, and tomatoes?

Explain how to do it in word please?

Again the crust will not change the probability.

Here the customer chooses 5 toppings out of 10 in C(10,5)=10!/(5!5!)=252 ways. This is the sample space.

If the customer is to have onions, jalapenos and tomatoes, he has two other choices out of 7 remaining toppings in C(7,2)=7!/(2!5!)=21 ways.

The probability is therefore:
21/252=1/12

To find the probability that a customer will order a five topping pizza including onions, jalapenos, and tomatoes, we need to determine the total number of possible combinations of five toppings and then calculate the number of combinations that include onions, jalapenos, and tomatoes.

Step 1: Determine the total number of possible combinations of five toppings.
Since the customer can choose from 10 different toppings (extra cheese, pepperoni, sausage, onions, banana peppers, jalapenos, tomatoes, fresh herbs, mushrooms, and black olives), to find the total number of possible combinations, we can use the formula for combinations, which is:
nCr = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items to be chosen.
In this case, n = 10 (number of toppings) and r = 5 (number of toppings to be chosen).

Therefore, the total number of possible combinations of five toppings is equal to:
10C5 = 10! / (5!(10-5)!) = 10! / (5!5!) = (10 × 9 × 8 × 7 × 6) / (5 × 4 × 3 × 2 × 1) = 252 combinations.

Step 2: Calculate the number of combinations that include onions, jalapenos, and tomatoes.
Since the customer must choose onions, jalapenos, and tomatoes as three of the toppings, we need to find the number of combinations for the remaining two toppings.
We can use the combinations formula again, but this time n = 7 (number of remaining toppings) and r = 2 (number of remaining toppings to be chosen).

Therefore, the number of combinations that include onions, jalapenos, and tomatoes is equal to:
7C2 = 7! / (2!(7-2)!) = 7! / (2!5!) = (7 × 6) / (2 × 1) = 21 combinations.

Step 3: Calculate the probability.
The probability is calculated by dividing the number of favorable outcomes (combinations that include onions, jalapenos, and tomatoes) by the total number of possible outcomes (total combinations).

Therefore, the probability that a customer will order a five topping pizza including onions, jalapenos, and tomatoes is:
P = Number of combinations that include onions, jalapenos, and tomatoes / Total number of possible combinations
P = 21 / 252
P ≈ 0.0833 or 8.33% (rounded to two decimal places).

Hence, the probability is approximately 8.33%.