Arug 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.)

The number of available colors is n = 7.
The number of colors that can be selected at a time among the 7 colors is r = 5.

This means that the number of selections of 5 colors from 7 colors at a time is ₇C₅.
By definition,


The number of color groupings is 21.

$527.7.if the following was the question  $527.7 is the answer.students who are trying to raise funds have an agreement with a local pizza chain. the chain has agreed to sell them pizzas at a discount, which the students can then resell to families in the local community for a profit. it is expected that of the 500 families in the community, at most 70% will buy pizza. based on a survey of their personal preferences, the students believe that they should order no more than 120 cheese pizzas, no more than 150 pepperoni pizzas, and no more than 100 vegetarian pizzas. they also want to make sure that at least 20% of the total pizzas are cheese and at least 50% of the pizzas are pepperoni. they make a profit of $1.45, $1.75, and $1.98, respectively, for each cheese, pepperoni, and vegetarian pizza they resell. how many pizzas of each type should they buy?

What's the rest of the problem? lol