Question

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. 840B. 42C. 21D. 7

Answer 1

Answer: 2520  

Step-by-step explanation:

We know that when repetition is not allowed while selecting r things from n things we use permutations.

The number of permutations of n things taken r at a time is given by ;-

$^nP_r=\dfrac{n!}{(n-r)!}$

Given : A rug manufacturer has decided to use seven compatible colors in her rugs.

i.e. Total number of colors : n= 7

However, in weaving a rug, only five spindles can be used.

So r= 5

Then, the number of color groupings using the seven colors taken five at a time are there :-'

$^7P_5=\dfrac{7!}{(7-5)!}\\\\=\dfrac{7\times6\times5\times4\times3\times2!}{2!}=2520$

Hence, the correct answer is 2520.

All the options are incorrect .