Sample Space Statistics Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
A restaurant offers 3 starters (soup, salad, bread), 4 mains (chicken, fish, beef, pasta), and 2 desserts (cake, fruit). How many different 3-course meals are possible? Do you need to list them all?

Solution

  1. 1
    Step 1: Use the multiplication principle: total meals = starters ×\times mains ×\times desserts = 3×4×2=243 \times 4 \times 2 = 24.
  2. 2
    Step 2: You do not need to list all 24 — the multiplication principle gives the count directly.
  3. 3
    Step 3: If needed, a tree diagram could systematically show all 24 combinations: 3 branches (starters) → each splits into 4 (mains) → each splits into 2 (desserts).

Answer

There are 3×4×2=243 \times 4 \times 2 = 24 different 3-course meals possible.
The multiplication principle (or counting principle) states that if there are mm ways to do one thing and nn ways to do another, there are m×nm \times n ways to do both. This extends to any number of independent choices and is fundamental to counting sample spaces.

About Sample Space

The sample space is the complete set of all possible outcomes for a probability experiment, listed without repetition. It forms the foundation for every probability calculation because the probability of any event is a fraction of the sample space.

Learn more about Sample Space →

More Sample Space Examples

Example 1 easy

List the sample space for rolling a standard six-sided die and flipping a coin simultaneously.

Example 3 medium

A password consists of one letter (A–E) followed by one digit (1–3). (a) List the entire sample spac

Example 4 hard

Two dice are rolled. (a) How many outcomes are in the sample space? (b) How many outcomes give a sum

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