You can choose chocolate,strawberryor vanilla frozen yogurt and red,blue,green sprinkles. A sundae has one yogurt flavor and two different colora of sprinkles. How many different kinds of sundaes can your order? List them
Is there 9 different possible kind of sundae?
yes 9 sundaes
a sunday has 1 of 3 flavours and 2 of 3 springles
Choose 1 from 3 and then 2 from 3
number of ways = C(3,1) x C(3,2) = 9 different ways
CRB,CRG,CBG
SRB, SRG, SBG
VRB, VRG, VBG
To find the number of different kinds of sundaes you can order, you need to multiply the number of yogurt flavors by the number of combinations of sprinkles.
Let's start with the yogurt flavors:
- You can choose from chocolate, strawberry, or vanilla, so there are 3 options.
Next, let's consider the combinations of sprinkles:
- You can choose two different colors of sprinkles from red, blue, and green. Since order doesn't matter, we will use combinations. The formula for combinations is nCr = n! / ((n-r)! * r!), where n represents the total number of options and r represents the number of items chosen.
- So, for choosing 2 colors out of 3, the number of combinations is 3C2 = 3! / ((3-2)! * 2!) = 3.
To find the total number of different kinds of sundaes, multiply the number of yogurt flavors by the number of combinations of sprinkles:
3 (yogurt flavors) * 3 (combinations of sprinkles) = 9.
Therefore, there are 9 different possible kinds of sundaes.
Here is the list of sundae options:
1. Chocolate yogurt with red and blue sprinkles
2. Chocolate yogurt with red and green sprinkles
3. Chocolate yogurt with blue and green sprinkles
4. Strawberry yogurt with red and blue sprinkles
5. Strawberry yogurt with red and green sprinkles
6. Strawberry yogurt with blue and green sprinkles
7. Vanilla yogurt with red and blue sprinkles
8. Vanilla yogurt with red and green sprinkles
9. Vanilla yogurt with blue and green sprinkles