A pizza parlor has 3 diffrebt crusts and 3 diffrent cheeses and 7 diffrent toppings . How many combinations are on a pizza with 3 topings 1 crust and 1 cheese ? Help please I got 42 and then was told I was wrong
To determine the number of combinations for a pizza with 3 toppings, 1 crust, and 1 cheese, you need to consider the number of options for each component and multiply them together.
Here's how you can find the answer step by step:
1. Start with the number of options for the toppings. Since you have 7 different toppings, you need to choose 3 of them. This can be calculated using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
In this case, n = 7 (number of toppings) and r = 3 (number of toppings to choose). Plugging these values into the formula, we get:
C(7, 3) = 7! / (3! * (7 - 3)!)
= (7 * 6 * 5) / (3 * 2 * 1)
= 35
2. Next, consider the number of options for the crust. As mentioned, there are 3 different crusts.
3. Lastly, determine the number of options for the cheese. Similar to the crust, there are 3 different cheeses.
Now, multiply the number of options for each component together:
Number of combinations = (Number of toppings) × (Number of crusts) × (Number of cheeses)
= 35 × 3 × 3
= 315
So, there are 315 different combinations for a pizza with 3 toppings, 1 crust, and 1 cheese.