A rug manufacturer has decided to use 7 compatible colours 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 colour groupings for sale. How many colour groupings using the seven colours taken five at a time are there? (This assumes that 5 different colours will go into each rug, i.e., there are no repetitions of colour.)
A) 120
B) 2,520
C) 6,740
D) 36

Question

Quizplus · Accepted Answer

The number of different colour groupings can be found by using the combination formula, which is: 
nCr = n! / r!(n-r)!
where n is the total number of colours (7) and r is the number of colours taken at a time (5). 
Plugging in the values, we get: 
7C5 = 7! / 5!(7-5)! 
= 7! / (5!2!) 
= (7x6x5x4x3x2x1) / (5x4x3x2x1x2x1) 
= 21x7 
= 147

Therefore, there are 2,520 different colour groupings using the seven colours taken five at a time.

A Rug Manufacturer Has Decided to Use 7 Compatible Colours