Question

A delicatessen makes a roast-beef-on-sourdough sandwich for which you can choose from eight condiments. a. How many different types of roast-beef-on-sourdough sandwiches can the delicatessen prepare? b. What is the minimum number of condiments the delicatessen must have available if it wishes to offer at least 1000
different types of roast-beef-on-sourdough sandwiches?

Answer 1

Analyzing the information, it is clear that to find the solutions of the problems it is necessary to perform the calculation of mathematical arrangements.

What are arrangements?

Correspond to a case of permutations, they are groupings that are formed with a number p of elements from a set of n elements. The elements of p must occupy ordered positions, where p ≤ n. The formula is:

• A = n!/(n-p)!

So, to solve the problems we do the following calculations:

A) 2^n =

2^8 = 256

B) We must pay attention to the statement, which asks for the minimum number of condiments required to prepare 1000 different sandwiches, so:

2^n $\geq$ 1000

n = 3

2^3 = 8

Find out more about arrangements here:

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