A pizza place has 5 different toppings. How many different pizzas can be made using a combination of 3 toppings per pizza
ABC
ABD
ABE
ACD
ACE
ADE
BCD
BCE
BDE
CDE
Count them. Then compute 5!/(3!2!)
To find out how many different pizzas can be made using a combination of 3 toppings per pizza, we can use the concept of combinations.
In this case, we have 5 different toppings and we want to choose 3 toppings for each pizza. The order in which the toppings are chosen does not matter, as we assume that any pizza with the same 3 toppings is the same.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where:
- n is the total number of items (toppings)
- r is the number of items chosen (toppings per pizza)
- ! denotes factorial, which means multiplying a number by every positive whole number less than itself down to 1.
Using the formula, we can calculate the number of combinations:
C(5, 3) = 5! / (3!(5-3)!)
= 5! / (3!2!)
= (5 x 4 x 3 x 2 x 1) / [(3 x 2 x 1) x (2 x 1)]
= (120) / (6 x 2)
= 120 / 12
= 10
Therefore, there are 10 different pizzas that can be made using a combination of 3 toppings per pizza.