A rug manufacturer has decided to use 7 compatible colors in her rugs. However, in weaving a rug, only 5 spindles can be used. In advertising, the rug manufacturer wants to indicate the number of different color groupings for sale. How many color groupings using the seven colors taken five at a time are there? (This assumes that 5 different colors will go into each rug, i.e., there are no repetitions of color.)
A) 120
B) 2,520
C) 6,740
D) 36

Question

Quizplus · Accepted Answer

This problem involves finding the number of combinations of 5 colors out of a set of 7 colors. This can be calculated using the formula for combinations, which is:

n! / (r! * (n-r)!)

where n is the total number of colors (7 in this case), and r is the number of colors being chosen (5 in this case).

Plugging in the numbers, we get:

7! / (5! * (7-5)!)
= (7 * 6 * 5 * 4 * 3) / (2 * 1)
= 2,520

Therefore, there are 2,520 different color groupings that can be used in the rugs. The answer is B.

A Rug Manufacturer Has Decided to Use 7 Compatible Colors