考试类型: Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

Cathy likes to wear 2 ribbons, each a different color. If she has 6 ribbons each of a different color, how many combinations of 2 different-colored ribbons can she select to wear?

A. 3

B. 6

C. 12

D. 15

E. 36

正确答案:D

解析:

It may be helpful to number the ribbons 1, 2, 3, 4, 5, and 6. Ribbon 1 can be worn with ribbons 2, 3, 4, 5, and 6, giving 5 combinations. Ribbon 2 can be worn with ribbons 3, 4, 5, and 6, giving 4 more combinations. (Do not recount ribbon 2 with ribbon 1, since that was counted in the first step.) Similarly, ribbon 3 can be worn with ribbons 4, 5, and 6, ribbon 4 can be worn with ribbons 5 and 6, and ribbon 5 can be worn with ribbon 6. The total number of combinations is 5 + 4 + 3 + 2 + 1 = 15.