Question

Committees The number of different committees of 2 students where the 2 students are selected from a class of $n$ students is given by $c(n)=\frac{1}{2}\left(n^{2}-n\right)$. If a biology class has 15 students, how many different committees having 2 students can be selected?

Name: Problem 83, Chapter 5: Intermediate Algebra for College Students
Uploaded: 2020-03-14T01:32:37-08:00
Duration: 53 s
Channel: Heather Zimmers
Description: Committees The number of different committees of 2 students where the 2 students are selected from a class of n students is given by c(n)=(1)/(2)(n^2-n). If a biology class has 15 students, how many different committees having 2 students can be selected?

   Committees The number of different committees of 2 students where the 2 students are selected from a class of $n$ students is given by $c(n)=\frac{1}{2}\left(n^{2}-n\right)$. If a biology class has 15 students, how many different committees having 2 students can be selected?

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 5, Problem 83

Instant Answer

Solved by Expert Heather Zimmers

03/14/2020

Step 1

We are also given that there are 15 students in the biology class. So, we need to find the number of different committees that can be selected from these 15 students. To do this, we can simply plug in the value of n (number of students) into the formula: Show more…

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Committees The number of different committees of 2 students where the 2 students are selected from a class of $n$ students is given by $c(n)=\frac{1}{2}\left(n^{2}-n\right)$. If a biology class has 15 students, how many different committees having 2 students can be selected?

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Key Concepts

Committee Selection

Committee selection is an application of combinations where a subset of individuals is chosen to form a committee. In problems like selecting 2 students from a class, the combination formula is applied to determine the number of possible committees.

Binomial Coefficient

The binomial coefficient, often denoted as C(n, k) or 'n choose k', is a mathematical formula used to calculate the number of combinations. Specifically, it is calculated as n! / (k!(n-k)!) and is used when order is not important in the selection process.

Combinations

Combinations involve selecting items from a larger set where the order of selection does not matter. This concept is central in combinatorics and is typically used to determine the number of ways to choose a subset of items from a larger group.

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