Question

how many different triple scoop cones canu make with 5 flavors of ice cream

Answer 1

By different, do you mean that the same flavor cannot be used for all three scoops of one cone?

Answer 2

right

Answer 3

like different combinations

Answer 4

like what make sense to me is 15..but when I write out the combination it doens make sense

Answer 5

What in the wording of the problem causes you to think that a cone that had 3 scoops of, say Vanilla, would not be allowed?

Answer 6

right

Answer 7

Hey, let's look at a smaller problem.

What if we were making two-scoop cones using the flavors of Vanilla and Chocolate.

Then, would we have: VV, CC, VC?

Would CV be considered different from VC?

Answer 8

it says a local shop has 5 flavors of ice cream, how many different triple scoop cones can they make?

Answer 9

no CV is the same as VC

Answer 10

What if we break this into 3 situations.

Case I: The 3 scoops are all alike.

There are 5 ways to do this. (Example: CCC, VVV, and so on for the 5 flavors).

@vmami0204 Before we go to Case II, do you follow Case One?

Answer 11

Case 2: all three scoops are different

The number of ways to choose three different flavors from a set of 5 flavors
is "five choose three".

C(5,3) = 10 (Use the combination formula.)

Answer 12

Case Three: two scoops the same, one scoop different

That would be 5 choices for two alike flavors with 4 choices left for the third scoop.
The number of possibilities is 5*4 = 20

Answer 13

In answer to the posted question:

how many different triple scoop cones can u make with 5 flavors of ice cream

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The sum of the case possibilities:

5 + 20 + 10 = 35 total.

@vmami0204 Check my logic and my work and determine if you agree. Thanks.