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Oliver is playing a game in which he has to choose one of three numbers ​(0 comma 1 comma or 8​) and then one of five vowels​ (a, e,​ i, o, or​ u). How many possible outcomes are​ there?

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Part 1
Draw a tree diagram of the outcomes. Choose the correct answer below.
A.
1
a
e
i
o
u
0
8
B.
0
a
e
i
o
u
1
8
C.
1
a
e
i
o
u
0
8
D.
a
e
i
o
0
1
a
e
i
o
u
u
8
a
e
i
o
u
Choose the correct answer below.There is/are(Type a whole number.)Choose the correct answer below.
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1 answer

To determine the total number of possible outcomes when choosing one number from the set {0, 1, 8} and one vowel from the set {a, e, i, o, u}, we can use the fundamental principle of counting.

  1. There are 3 choices for the numbers: 0, 1, or 8.
  2. There are 5 choices for the vowels: a, e, i, o, or u.

To find the total number of outcomes, you multiply the number of choices for the first selection by the number of choices for the second selection:

\[ \text{Total outcomes} = (\text{Number of choices for numbers}) \times (\text{Number of choices for vowels}) = 3 \times 5 = 15 \]

Tree Diagram:

Now, let's create the tree diagram. Each number will branch out to the five vowels:

           Start
         /   |    \
       0     1     8
      /|\   /|\   /|\
     a e i o u a e i o u a e i o u

So, the complete sets of outcomes are as follows:

  • For 0: 0a, 0e, 0i, 0o, 0u (5 outcomes)
  • For 1: 1a, 1e, 1i, 1o, 1u (5 outcomes)
  • For 8: 8a, 8e, 8i, 8o, 8u (5 outcomes)

Conclusion:

The total number of possible outcomes is 15.

Choose the correct answer: 15.

For the tree diagram format that matches your choices, none of the given options are completely structured correctly based on standard tree diagrams, but the idea of branching them by numbers leading to vowels is what we illustrated. If we are to select which option gives a similar idea, none of them are formatted correctly as a complete tree structure. However, based on your options, the grouping belonging to numbers first before vowels, best resembles option A.