Question

The Combinatorial Creamery features 10 flavors of ice cream. Their waffle cone special has four scoops of different flavors stacked on top of each other on a waffle cone. You can decide the order in which the scoops are stacked. How many different waffle cone specials could you possibly order from the Combinatorial Creamery?

Answer 1

Using the Fundamental Counting Theorem, it is found that you could order 240 different waffle cone specials could you possibly order from the Combinatorial Creamery.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

For this problem, we have that the parameters are found as follows:

• 10 flavors, hence $n_1 = 10$.

• The order of the scoops can be chosen, with 4! possible orderings, hence $n_2 = 4! = 24$.

Thus, the number of cones is given by:

N = 10 x 24 = 240.

240 different waffle cone specials could you possibly order from the Combinatorial Creamery.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

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