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Show Programs Three bands and two comics are performing for a student talent show. How many different programs (in terms of order) can be arranged? How many if the comics must perform between bands?

120 ; 12

Intro Stats / AP Statistics

Chapter 4

Probability and Counting Rules

Section 4

Counting Rules

Sampling and Data

Probability Topics

Sumbul A.

December 1, 2020

December 2, 2020

Temple University

Piedmont College

Cairn University

Lectures

0:00

01:05

Six performers are to pres…

01:34

Use the Fundamental Counti…

01:43

Use the fundamental princi…

00:46

Five singers are to perfor…

01:04

00:42

Tell whether each situatio…

02:18

Programming Music A zydeco…

01:22

00:40

Tell whether the question …

Use an appropriate rule of…

Nine bands have volunteere…

05:49

Selecting Musicals How man…

01:33

A program is planned to ha…

Solve by the method of you…

01:08

00:29

01:45

01:37

Nine comedy acts will perf…

02:22

Arranging Books Five diffe…

So this particular problem is an application off the fundamental counting rule. So according to this problem, you have three bends and two comics, and they will be performing in a talent show. First question is how many different programs in terms, off order or arrangements can be created. The second question. If we want the comics to perform in between bands, then how many possible programs can be created? So we called the fundamental counting rule, which basically says, If you have a sequence of events where the first event has case of one possibilities, the second event has case of two possibilities and so on. The in event has case of impossibilities, then the total number off possibilities off the sequence will be case of one times case. Him, too, and so on times. Case of And so for that first question way have three bench and to call mix. There are five sluts in the program to be filled in right, the first performer, second performer and so on, up to the fifth performer for the first performer, that very first slot there we have five choices or five possibilities. Anyone off the three bands in two comics can perform first for the second slot. We have four choices because one of them is already performing first. Third Slud. We will have three choices for its lead. Two choices in the Fifth Slut. One choice left. According to the fundamental accounting rule, the total number off arrangements will be five times four times three times to Time Schwann, which is equal to five factorial, which is equal to 120 different arrangements or different programs that you can create. For the second question, we want the comics to perform in between bands. OK, we still have the same five performers in the same five sluts, but we want the comics to perform in between the bends. So the second in the fort performer we'll have to be got mix. So let's look at the band first. First performer will be a band, and we would have three choices for that. Since there are three bands, third performer will have to be abandoned. Swell. There will be two choices left because one band is performing first in the Fifth Slut, you have one band left to perform for the comics. The second performer, which has to be a comic. You have two choices. The fort performer, also a comic. You have one choice left According to the fundamental counting rule, there will be three times, two times, two times, one times one different arrangements. Or we can say that there would be, in this case, 12 different programs that you can you can create.

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