if i had 15 toppings how many different 5 topping pizzas can I make without a repeat?
15C5
To determine the number of different 5-topping pizzas you can make without repeats from a pool of 15 toppings, you can use the concept of combinations.
The formula for calculating the number of combinations is:
n C r = n! / (r! * (n-r)!)
In this case, n represents the total number of toppings (15), and r represents the number of toppings you want to choose for the pizza (5).
Plugging in the values, the calculation becomes:
15 C 5 = 15! / (5! * (15-5)!)
= 15! / (5! * 10!)
= (15 * 14 * 13 * 12 * 11) / (5 * 4 * 3 * 2 * 1)
= 3,003
Therefore, you can make 3,003 different 5-topping pizzas without repeats from a pool of 15 toppings.
To find the number of different 5-topping pizzas you can make without repeats from 15 toppings, you can use the concept of combinations.
The formula for combinations is expressed as C(n, r), where n represents the total number of items to choose from, and r represents the number of items being chosen at a time.
In this case, n represents the 15 toppings you have, and r represents the 5 toppings you want to choose for each pizza.
So, you need to calculate C(15, 5).
The formula for combinations is given by:
C(n, r) = n! / (r! * (n-r)!)
To apply the formula, you need to calculate the factorials of the numbers involved:
n! is the factorial of n, which means multiplying all the positive integers from 1 to n.
In this case, you need to calculate 15!, which is 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1.
r! is the factorial of r, which means multiplying all the positive integers from 1 to r.
In this case, you need to calculate 5!, which is 5 * 4 * 3 * 2 * 1.
And (n-r)! is the factorial of (n-r), which means multiplying all the positive integers from 1 to (n-r).
In this case, you need to calculate (15-5)!, which is 10!.
Now, you can substitute the values into the combinations formula:
C(15, 5) = 15! / (5! * 10!)
Performing the calculation, you will get the answer for the number of different 5-topping pizzas you can make without repeats from 15 toppings.