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A conductor needs 5 cellists and 5 violinists to play at diplomatic event. To do this, he ranksthe orchestra's 10 cellists and 16 violinists in order of musical proficiency. What is the ratio of thetotal cellist rankings possible to the total violinist rankings possible?

$1 : 5765760$

Calculus 2 / BC

Algebra

Chapter 9

Sequences, Probability and Counting Theory

Section 5

Counting Principles

Series

Introduction to Sequences and Series

Introduction to Combinatorics and Probability

Missouri State University

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

01:18

A conductor needs 5 cellis…

03:06

Predict/Calculate Two viol…

07:48

A violin string has a leng…

05:43

01:43

Use the fundamental princi…

00:47

These problems involve com…

01:22

05:52

14:57

If Mozart composed his fir…

this problem is concerning whether to use a combination or a permutation to solve a real life application. So the question acts. A conductor needs five cellists and five violinist to play a diplomatic event, and the orchestra has 10 cellists and 16 violinists, and he wants to rank them in order of musical proficiency and asks, What's the ratio of total cellist drinking's possible and total violinist rankings possible? So first, let's break this problem down. Since the questions asking for total cellist rankings possible and total violinist rankings possible in a ratio, let's first find those two values. So the total cellist rankings possible once when a problem asks for rankings. That means that order matters and the and the funk and the counting method that we use when order matters is a permutation. Soto find the total cellist ranking possible. We would need to d'oh ah, permutation. However he is not. It's easy to go 10. She's five with a permutation, but that's just incorrect because it's not ranking those five cellists as ranking the whole orchestra. So instead, it would just be 10 factorial because we always start with 10 factorial incest. The whole group of cellists before dividing by anything terminal cases. So now we have 10 factorial. Let's find the total violinist rankings possible, and that ends up being 16 factorial because they're 16 violinists and you would not divide because you're not removing any cases. So to find the final ratio, you need to divide by the smaller number, which ends up being 10 factorial. So it's 1 to 16 factorial over 10 factorial and bye Factorial Rules ends up being 1 to 60 cents 15 times 14 times, 13 times 12 times 11 which all comes out to 12 ah, 576 576 zero. And that's the final answer. So the main takeaway is don't get distracted by the first part of the problem because the five, uh, the groups of five don't

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