In a sports competition there are (3) team-name options and (6) jersey-color options. How many team identities can be made by choosing one name and one color?

Correct answer: (18) identities

The direct answer is option A: 18 identities. An identity is formed by selecting exactly one team name and exactly one jersey color. There are 3 choices for the name. For each chosen name, there are 6 possible colors, so the multiplication principle gives \(3\times6=18\). Option A is correct because every name can be combined with every color. Option B, 9, does not result from the required calculation; adding the categories would also be inappropriate. Option C, 12, is another incorrect product or partial count and does not include all name-color pairs. Option D, 36, reverses no useful rule but doubles the correct result; there are not 6 choices for both parts. The choices are independent, so a name does not reduce or change the number of available colors. Count a few examples if needed: name 1 has 6 identities, name 2 has 6, and name 3 has 6; hence \(6+6+6=18\), the same as \(3\times6\).