A Rug Manufacturer Has Decided to Use Seven Compatible Colors

Multiple Choice

A rug manufacturer has decided to use seven compatible colors in her rugs. However,in weaving a rug,only five 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 five different colors will go into each rug-in other words,there are no repetitions of color.)

A) 7
B) 21
C) 840
D) 42