A child has 2 shirts (one red and one blue) and 3 types of pants (jeans, khakis, and shorts). List all the possible combinations of outfits consisting of one shirt and one pair of pants. Display your answer in a table format.
To find all possible combinations of outfits, we pair each shirt with each type of pants. The child has 2 shirts (Red, Blue) and 3 types of pants (Jeans, Khakis, Shorts).
By using the fundamental principle of counting, the total number of possible outfit combinations is = 6. We can systematically list these combinations by taking one shirt at a time and pairing it with all available pants.
The table below displays all the possible outfit combinations:
| Shirt | Pants | Outfit Combination |
|---|---|---|
| Red | Jeans | Red Shirt & Jeans |
| Red | Khakis | Red Shirt & Khakis |
| Red | Shorts | Red Shirt & Shorts |
| Blue | Jeans | Blue Shirt & Jeans |
| Blue | Khakis | Blue Shirt & Khakis |
| Blue | Shorts | Blue Shirt & Shorts |
Explanation
The question requires listing the sample space for a multi-step experiment involving the selection of a shirt and then a pair of pants. By applying the fundamental principle of counting, the total number of combinations is the product of the number of choices for each step (2 shirts × 3 pants = 6 combinations). A table is used to clearly display each unique pairing.
Solution Steps
Step 1: Identify the available shirts: Red, Blue (2 options).
Step 2: Identify the available pants: Jeans, Khakis, Shorts (3 options).
Step 3: Calculate total combinations: = 6.
Step 4: List and tabulate all 6 combinations systematically by pairing each shirt with every type of pants.