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

$1 : 5765760$

Calculus 2 / BC

Precalculus

Chapter 11

Sequences, Probability and Counting Theory

Section 5

Counting Principles

Series

Introduction to Combinatorics and Probability

Piedmont College

Oregon State University

Boston College

Lectures

07:16

In mathematics, a continuo…

04:09

02:48

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…

01:22

00:47

These problems involve com…

00:54

You are one of 10 students…

01:34

In a group of 20 musicians…

01:11

If Mozart composed his fir…

Okay, so 10 cellists are being ranked and 16 violinists are being ranked and the number of ways to rank the 10 cellists is 10 factorial and the number of ways to rank. The 16 violinist is 16 factorial and were asked to find the ratio of these. So we have 10 factorial over 16 factorial now to simplify it. Keep in mind that 10 factorial is 10 times nine times eight et cetera. All the way down two times two times one and 16 factorial 16 times, 15 times 14 10 13 times 12 tons 11 times 10 9 et cetera. All the way down to one so we could cancel from the top of the bottom. The 10 the 9 38 and so on. All the way down to one. And all we have left in this ratio is one over 16 times, 15 times, 14 times, 13 times, 12 times 11. And when you work that out, you get the ratio one to five million 765,000 7 60

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