Question: 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).