ASVAB Study Guide4.Percent Change
Calculating the total number of possible outcomes for a sequence of independent events.
Total Outcomes = $$n_1 \times n_2 \times \ldots \times n_k$$
If one event can occur in m ways and a second independent event can occur in n ways, the total events occur in $$m \times n$$ ways.
Example
A restaurant offers 3 appetizers and 4 main courses. How many different combinations of 1 appetizer and 1 main course can you order?
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Step 1: Identify the number of choices for the first event: 3
Step 2: Identify the number of choices for the second event: 4
Step 3: Multiply the choices together: $$3 \times 4 = 12$$ combinations
Practice problems
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Problem 1
A person is picking an outfit. They have 5 shirts, 3 pairs of pants, and 2 pairs of shoes to choose from. How many unique outfits can they create?
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Answer: 30 outfits
Step 1: Identify the choices: 5 shirts, 3 pants, 2 shoes
Step 2: Multiply the independent choices together: $$5 \times 3 = 15$$
Step 3: Multiply by the remaining choice: $$15 \times 2 = 30$$ outfits
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Problem 2
A tech company requires security pins to consist of exactly 1 letter followed by 2 digits $$(0-9)$$. How many distinct pins can be made?
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Answer: 2600 pins
Step 1: Count choices for letter: 26. Count choices for each digit: 10
Step 2: Set up the multiplication: $$26 \times 10 \times 10$$
Step 3: Calculate the total outcomes: 2600 pins
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Problem 3
A coin is flipped three times. How many total possible outcomes are there for the sequence of flips?
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Answer: 8 outcomes
Step 1: Identify outcomes per flip: 2 (Heads or Tails)
Step 2: Set up the multiplication for three independent flips: $$2 \times 2 \times 2$$
Step 3: Calculate the total outcomes: 8 outcomes
Identify the number of available choices for each independent stage and multiply them sequentially.