For this Big Problem, we’re going to investigate the different combinatorial formulas to figure out why they are the way they are. Using Zoom! (1) Suppose you are organizing a Zoom meeting and invite ten people. You don’t know who all is coming so you watch people sign on one at a time. How many possibilities are there for the first, second, and third people to sign on? (2) What formula did you use for question one, and why? (3) Suppose you are running late so by the time you log on three people have already arrived. How many possibilities are there for which three people are logged on? (4) What formula did you use for question three, and why? (5) You know that Person A, Person B, and Person C logged on before you but you don’t know who came first. How many possibilities are there for the order of A, B, and C to have signed on before you? (6) What formula did you use for question five, and why? (7) Look at your answers to one, three, and five. Write an equation of the form x×y = z using these numbers. Do you have an explanation for this equation? (8) Look at your answers to two, four, and six. Write an equation of the form x × y = z using those three formulas. Do you have an explanation for this equation?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

For this Big Problem, we’re going to investigate the different combinatorial formulas to
figure out why they are the way they are. Using Zoom!

(1) Suppose you are organizing a Zoom meeting and invite ten people. You don’t know
who all is coming so you watch people sign on one at a time. How many possibilities
are there for the first, second, and third people to sign on?

(2) What formula did you use for question one, and why?

(3) Suppose you are running late so by the time you log on three people have already
arrived. How many possibilities are there for which three people are logged on?

(4) What formula did you use for question three, and why?

(5) You know that Person A, Person B, and Person C logged on before you but you don’t
know who came first. How many possibilities are there for the order of A, B, and C
to have signed on before you?

(6) What formula did you use for question five, and why?

(7) Look at your answers to one, three, and five. Write an equation of the form x×y = z
using these numbers. Do you have an explanation for this equation?

(8) Look at your answers to two, four, and six. Write an equation of the form x × y = z
using those three formulas. Do you have an explanation for this equation?

Expert Solution

Step 1

Given in a zoom meeting ten people are invited, three persons logged on the meeting.

A permutation is an arrangement of a given number of objects in some given number of places in a definite order.

If there are $n$ objects and $r$ places to arrange the $n$ objects, then there are ${}^{n}P_{r} = \frac{n!}{(n - r)!}$ arrangements or permutations.

A combination is a group of some specific number of objects out of all the given objects. In combination the order of the object in the group does not matter.

If there are $n$ objects and groups of $r$ objects are to be formed, then there are ${}^{n}C_{r} = \frac{n!}{r! (n - r)!}$ groups or possible combinations.