Question

Committees The number of different committees of 3 students where the 3 students are selected from a class of $n$ students is given by $c(n)=\frac{1}{6} n^{3}-\frac{1}{2} n^{2}+\frac{1}{3} n$. If an art class has 10 students, how many different committees having 3 students can be selected?

Name: Problem 84, Chapter 5: Intermediate Algebra for College Students
Uploaded: 2022-01-09T20:04:45-08:00
Duration: 2 min 4 s
Channel: Hunza Gilgit
Description: Committees The number of different committees of 3 students where the 3 students are selected from a class of n students is given by c(n)=(1)/(6) n^3-(1)/(2) n^2+(1)/(3) n. If an art class has 10 students, how many different committees having 3 students can be selected?

   Committees The number of different committees of 3 students where the 3 students are selected from a class of $n$ students is given by $c(n)=\frac{1}{6} n^{3}-\frac{1}{2} n^{2}+\frac{1}{3} n$. If an art class has 10 students, how many different committees having 3 students can be selected?

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 5, Problem 84

Instant Answer

Solved by Expert Hunza Gilgit

01/09/2022

Step 1

We can do this by plugging n = 10 into the given formula: c(10) = (1/6) * 10^3 - (1/2) * 10^2 + (1/3) * 10 c(10) = (1/6) * 1000 - (1/2) * 100 + (1/3) * 10 Show more…

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Committees The number of different committees of 3 students where the 3 students are selected from a class of $n$ students is given by $c(n)=\frac{1}{6} n^{3}-\frac{1}{2} n^{2}+\frac{1}{3} n$. If an art class has 10 students, how many different committees having 3 students can be selected?

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Key Concepts

Substitution into Algebraic Formulas

Substitution in algebra involves replacing the variable(s) in a formula with known values to compute the result. In problems involving committee selection, this often means plugging in the number of students into the combination formula to find the number of possible committees.

Combination

A combination is a method in combinatorics used to determine how many ways a subset of items can be selected from a larger set without considering the order. It is typically represented as 'n choose r' where n is the total number of items and r is the number of items to select.

Binomial Coefficient

The binomial coefficient, expressed as C(n, r) = n! / (r! (n - r)!), calculates the number of ways to select r items from a set of n, which is fundamental when forming committees or groups from a larger population.

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