Question

a class is choosing a president, a vice president, and a treasurer.
there are three students running for president: linda, maria, and ann.
there are two students running for vice president: john and bob.
there are two students running for treasurer: jessica and amanda.
the tree diagram below shows the possible outcomes. use the diagram to answer the questions.
(a) how many outcomes are there?
□ outcome(s)
(b) how many outcomes have both bob and amanda being chosen?
□ outcome(s)
(c) how many outcomes do not have linda being chosen?
□ outcome(s)

Explanation:

Part (a)

Step1: Count outcomes per president

For each president (Linda, Maria, Ann), count their outcomes. Linda has 4, Maria has 4, Ann has 4.

Step2: Total outcomes

Sum the outcomes: \( 4 + 4 + 4 = 12 \).

Step1: Identify relevant outcomes

Look for outcomes with Bob (Vice President) and Amanda (Treasurer). For each president (Linda, Maria, Ann), check.

Step2: Count such outcomes

Linda: (Linda, Bob, Amanda); Maria: (Maria, Bob, Amanda); Ann: (Ann, Bob, Amanda). So 3 outcomes.

Step1: Outcomes without Linda

Linda has 4 outcomes. Total outcomes are 12. Subtract Linda's outcomes: \( 12 - 4 = 8 \).

Answer:

12

Part (b)