A test consists of 14 questions that are divided into three sections. There are 6 questions in the first section, 3 in the second section, and 5 in the third section. A student is required to answer 7 out of these 14 questions. In how many ways can the student answer 7 questions if the students select 2 from the first section, 3 from the second section, and 2 from the third section?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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. A test consists of 14 questions that are divided into three sections. There are 6 questions
in the first section, 3 in the second section, and 5 in the third section. A student is
required to answer 7 out of these 14 questions. In how many ways can the student
answer 7 questions if the students select 2 from the first section, 3 from the second
section, and 2 from the third section?

Expert Solution
Step 1

A test consist  14  questions 

Test is divided into three sections

First section have 6 question

Second section have 3 question

Third section have 5 question  

We have to find the number of ways that the student answer 7 question by selecting 2 from the first section, 3 from the second section and 2 from the third section

Combination:

Number of ways to select r things out of n=nCr.

where, nCr=n!r!n-r!

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