## Related questions with answers

A radio show plays the top 10 musical hits of the previous week. During the first full week of last January, these 10 hits were chosen from 70 possibilities, and they were played in order of increasing popularity. How many possible orders were there? Note: Since calculators cannot evaluate large factorials, use the approximation given by the formula $n ! \approx \sqrt{2 \pi n}\left(\frac{n}{e}\right)^n$.

Solutions

VerifiedWe have a radio that plays the top $10$ musical hits. We have to determine how many possible orders were there. These hits were chosen from $70$ possibilities, and they were played in order of increasing popularity. We have to determine how many possible orders were there.

*When we use combinations instead of permutations?*

Action 1.

First we choose 10 tracks out of 70, in no particular order.

The number of ways of doing this is ${}_{70}C_{10}.\\\\$ Action 2.\ Arrange the 10 tracks in order of increasing popularity.\\ Once chosen, there is only {\bf one} arrangement of these tracks which represents the order by increasing popularity.\\

By the Multiplication Principle, the number of total arrangements , then, is \qquad \\${}*{70}C*{10}\cdot 1.

$

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Advanced Mathematics: Precalculus with Discrete Mathematics and Data Analysis

ISBN: 9780395551899Brown#### Precalculus: Mathematics for Calculus

7th Edition•ISBN: 9781305253810James Stewart, Lothar Redlin, Saleem Watson#### Big Ideas Math Algebra 2: A Common Core Curriculum

1st Edition•ISBN: 9781608408405Boswell, Larson## More related questions

- calculus
- calculus
- calculus
- calculus
- calculus
- calculus

1/4

- calculus
- calculus
- calculus
- calculus
- calculus
- calculus

1/7