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Freight Train Cars In a train yard there are 4 tank cars, 12 boxcars, and 7 flatcars. How many ways can a train be made up consisting of 2 tank cars, 5 boxcars, and 3 flatcars? (In this case, order is not important.)
Intro Stats / AP Statistics
Chapter 4
Probability and Counting Rules
Section 4
Counting Rules
Sampling and Data
Probability Topics
Adnan M.
December 5, 2020
Missouri State University
University of North Carolina at Chapel Hill
Idaho State University
Lectures
0:00
02:16
Solve each problem. See Ex…
02:14
In how many ways can a com…
00:26
Tell whether each situatio…
00:35
These exercises involve di…
01:06
In how many ways can 7 ath…
01:21
In how many different ways…
02:21
Agency Cases An investigat…
00:31
From a pool of 7 secretari…
02:49
Stacking Boxes In how many…
00:47
These problems involve dis…
04:49
Selecting a Committee Ther…
00:59
01:19
In how many ways can 5 dif…
00:27
How many different ways ar…
00:46
A car can be ordered in an…
00:48
These problems involve per…
01:41
Use the fundamental princi…
01:40
How many ways are there fo…
00:30
In how many ways can 7 peo…
01:03
In how many ways can 5 new…
your four tank cars. 12 boxcars in seven flat cars in a train yard. How many ways can you form a train with two tank cars, five boxcars and three flatcars? Assume for this question. That order is not important. They're two concepts did we will use for this problem The combination rule, which states that the number of combinations of and taken our is equal to n factorial over and minus. R factorial times r. Factorial Also, we need the fundamental counting room. He says that, you know sequence of an event where there are que one possibilities for the first event K two possibilities for the second event and so on. The total number off possibilities off the sequence is K one time skate too times and so on k n. So the number of ways we can choose to thank cars from four or there is not important important is going to be combination. Four. Taken to at the time the number of ways we can choose five boxcars from 12 is combination 12 stick and five number of ways. We can choose three flat cars from seven. It's combination seven taken three at the time, according to the fundo mental counting rule. To find a number of ways we conform the train we just moved. Apply these factors. You can use your calculator to find the value of each of those combinations. We can use the combination rule for each one of them as well. So this first factor will be four factorial over two factorial times, two factorial times 12 factorial over seven factorial times five Pictorial timeshare Been factorial over four factorial Times Street factorial And you can use your calculator to evaluate this. It's six times 7 92 times 35 which is equal to 166,000 320 different ways to form the train.
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