Students at Rise Middle School are required to wear uniforms to school. Each student has the choice of wearing blue or khaki pants and a red, white, or green shirt. The student council wants to add black pants and maroon shirts to the school's uniform outfit choices. Which of the following is the number of new outfits that the students would have to choose from?

Rationale

Students would have 6 new outfit combinations with the addition of black pants and maroon shirts.

With the introduction of black pants and maroon shirts, the total number of outfit combinations increases. Initially, students could choose from 2 pant options (blue or khaki) and 3 shirt options (red, white, or green), resulting in 6 combinations. Adding 1 new pant option and 1 new shirt option increases the choices to 3 pant options and 4 shirt options, yielding a total of 12 combinations (3 x 4 = 12).

A (3) YOUR ANSWER

This choice reflects a misunderstanding of the combination formula. The number 3 might represent only the number of additional clothing items (black pants or maroon shirts) or a limited selection but does not account for all possible outfits that can be created with the new options.

B (5) YOUR ANSWER

This option undercounts the potential outfit combinations. While it may seem plausible if considering just one new pant or shirt added, it neglects the full multiplication of all available options that arise from the inclusion of both black pants and maroon shirts.

C (6) CORRECT

This number might seem accurate based on the original uniform choices of blue or khaki pants with red, white, or green shirts (2 pants x 3 shirts = 6). However, it does not include the new options introduced, which are essential for calculating the expanded outfit possibilities.

D (7) YOUR ANSWER

This number incorrectly assumes only a minimal increase in outfit combinations. It may stem from counting one additional option without fully considering the total combinations resulting from all possible pairs of pants and shirts after the new items are added.

Conclusion

When the student council adds black pants and maroon shirts, students gain a total of 12 outfit combinations, derived from multiplying the number of pant options (3) by the number of shirt options (4). This extensive range of choices encourages individuality while adhering to uniform guidelines, highlighting the importance of calculating potential combinations correctly.

Students would have 6 new outfit combinations with the addition of black pants and maroon shirts.

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