Question

\text {Solve each problem involving combinations.} Hamburger Choices Howard's Hamburger Heaven sells hamburgers with cheese, relish, lettuce, tomato, mustard, or ketchup. How many different hamburgers can be made that use any 3 of the extras?

Name: Problem 53, Chapter 8: A Graphical Approach to College Algebra
Uploaded: 2020-07-23T01:30:13-08:00
Duration: 1 min 35 s
Channel: Ankit Gupta
Description: Solve each problem involving combinations. Hamburger Choices Howard's Hamburger Heaven sells hamburgers with cheese, relish, lettuce, tomato, mustard, or ketchup. How many different hamburgers can be made that use any 3 of the extras?

   \text {Solve each problem involving combinations.}
Hamburger Choices Howard's Hamburger Heaven sells hamburgers with cheese, relish, lettuce, tomato, mustard, or ketchup. How many different hamburgers can be made that use any 3 of the extras?

A Graphical Approach to College Algebra

John… 6th Edition

Chapter 8, Problem 53

Instant Answer

Solved by Expert Ankit Gupta

07/23/2020

Step 1

The order of selection does not matter here, so we use the combination formula. The combination formula is given by C(n, r) = n! / r!(n-r)!, where n is the total number of items, and r is the number of items to choose. Show more…

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\text {Solve each problem involving combinations.} Hamburger Choices Howard's Hamburger Heaven sells hamburgers with cheese, relish, lettuce, tomato, mustard, or ketchup. How many different hamburgers can be made that use any 3 of the extras?

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Key Concepts

Combination

A combination is a selection of items from a larger set where the order does not matter. It is calculated using the formula n choose k, written as nCk = n! / (k!(n-k)!), where n is the total number of items and k is the number of items selected.

Factorial

A factorial, denoted as n!, is the product of all positive integers from 1 up to n. Factorials are a fundamental concept in combinatorics, appearing in the calculation of combinations and permutations to account for the various arrangements of items.

Binomial Coefficient

The binomial coefficient, represented as nCk, quantifies the number of ways to choose k elements from a set of n elements without regard to order. It is a key concept in both combinatorics and algebra, particularly in the expansion of binomials and counting problems.

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