Question

A girls' choir is choosing a concert uniform. They can pick red, green, or purple sweaters, and they can pick tan or black skirts.
The shoes only come in
gold and black.

How many different combinations can be made? (What is the sample size?) Make a tree diagram to find the result.

7 ?
8 ?
12 ?
18 ?

Answer 1

Answer:  C) 12

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Explanation:

There are 3 colors of sweaters {red, green, purple} and 2 colors of skirts {tan, black}

So far there are 3*2 = 6 different outfit combinations. Imagine a table with 3 rows representing the sweater colors and 2 columns representing the skirt colors. There would be 6 cells in the table representing each possible combination. One cell would have (red sweater, tan skirt) for instance.

For each of those 6 combinations, we also have 2 shoe colors. So overall we have 6*2 = 12 outfit combinations

The tree diagram is shown below. Note how there are 3*2*2 = 12 different paths to follow.