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Tia's Snow Cone Xpress offers 2 sizes (small or huge), 4 flavors (cherry, vanilla,
strawberry, bubble gum), and 3 glow-in-the-dark spoon choices (green, purple, red).
1) Write out all possible outcomes in an organized fashion. How many different
possible combinations are there in total?.
2) What method did you use to make this determination? Why did you use that
method?
3) How many different snow cones include the cherry flavor and a green spoon?
How did you come up with this answer?

Sagot :

Answer:

1) Small-Cherry-Green, 2) Small-Cherry-Purple, 3) Small-Cherry-Red, 4) Small-Vanilla-Green, 5) Small-Vanilla-Purple, 6) Small-Vanilla-Red, 7) Small-Strawberry-Green, 8) Small-Strawberry-Purple, 9) Small-Strawberry-Red, 10) Small-bubble gum-Green, 11) Small-Bubble gum-Purple, 12) Small-Bubble gum-Red , 13) Huge-Cherry-Green, 14) Huge-Cherry-Purple, 15) Huge-Cherry-Red, 16) Huge-Vanilla-Green, 17) Huge-Vanilla-Purple, 18) Huge-Vanilla-Red, 19) Huge-Strawberry-Green, 20) Huge-Strawberry-Purple, 21) Huge-Strawberry-Red, 22) Huge-Bubble gum-Green, 23) Huge-Bubble gum-Purple, 24) Huge-Bubble gum-Red

b) 24

2) Tree diagram method

b) Each unique snow cone has an element of each category

3) 2

i) By counting

ii) By finding out the possible combinations

Step-by-step explanation:

The details of the options at Tia's Snow Xpress includes;

2 (different) sizes; Small or huge size

4 (different) flavors; Cherry, vanilla, strawberry, bubble gum

3 glow-in-the-dark spoon choices; Green, purple, red

1) Let the 'a' represent the small size let 'b' represent the huge size, let 'c' represent cherry, let 'v' represent vanilla, let 's' represent strawberry, let 'b' represent bubble gum, let '1' represent green, let '2' represent purple and let '3' represent red, we have;

The possible outcomes are;

ac1, ac2, ac3, av1, av2, av3, as1, as2, as3, ab1, ab2, ab3

bc1, bc2, bc3, bv1, bv2, bv3, bs1, bs2, bs3, bb1, bb2, bb3

With the use of MS Word, we have;

1) Small-Cherry-Green, 2) Small-Cherry-Purple, 3) Small-Cherry-Red, 4) Small-Vanilla-Green, 5) Small-Vanilla-Purple, 6) Small-Vanilla-Red, 7) Small-Strawberry-Green, 8) Small-Strawberry-Purple, 9) Small-Strawberry-Red, 10) Small-bubble gum-Green, 11) Small-Bubble gum-Purple, 12) Small-Bubble gum-Red

13) Huge-Cherry-Green, 14) Huge-Cherry-Purple, 15) Huge-Cherry-Red, 16) Huge-Vanilla-Green, 17) Huge-Vanilla-Purple, 18) Huge-Vanilla-Red, 19) Huge-Strawberry-Green, 20) Huge-Strawberry-Purple, 21) Huge-Strawberry-Red, 22) Huge-Bubble gum-Green, 23) Huge-Bubble gum-Purple, 24) Huge-Bubble gum-Red

Therefore;

b) There are 24 different combinations in total

2) The method used to find the combinations is a tree diagram with branches extending from, the size of the Snow Cone Xpress to the choices for the glow-in-the-dark spoons

b) The method was used because of there are more than two categories each with different number of items and each unique Snow Cone Xpress option comprises of an element of each category

3) The number of Snow Cones that includes the cherry flavor and a green spoon = 2 different Snow cones

b) The answer can be arrived at by either;

i) Counting from the listed snow cone options

ii) Noting that a setting the only options for flavor as cherry and the only option for the glow-in-the-dark spoon as green and then combining both categories into one category option with the connection 'and' we have the possible combination as 3 items taking 2 at a time less the combination of the small and huge snow cones as follows;

Combinations = ₃C₂ - 1 = 2

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