An examinee is required to answer 6 questions out of 12,...

Name: Problem 40, Chapter 3: Business Mathematics and Statistics
Uploaded: 2021-07-22T02:02:54-08:00
Duration: 1 min 44 s
Channel: Goutam Chand
Description: An examinee is required to answer 6 questions out of 12, which are divided into two groups each containing 6 questions. He is not allowed to answer more than 4 questions from any group. In how many ways, can he answer 6 questions?

An examinee is required to answer 6 questions out of 12, which are divided into two groups each containing 6 questions. He is not allowed to answer more than 4 questions from any group. In how many ways, can he answer 6 questions?

Key Concepts

Summation Principle

The summation principle states that if there are multiple mutually exclusive cases or scenarios, the total number of outcomes is the sum of the outcomes of each case. This principle is applied after performing case analysis to combine the counts from the various valid selection scenarios into one total count.

Case Analysis in Counting

Case analysis involves breaking down a complex counting problem into several distinct scenarios that together cover all possibilities. By considering each scenario separately—often based on varying counts selected from different groups—and then summing the counts, a comprehensive solution can be achieved.

Combinatorial Selection

This concept involves choosing a subset of items from a larger set without regard to the order of selection. In problems like these, it is essential to count the possible groups (combinations) of items (questions) that can be selected, often using binomial coefficients to perform the calculations.

Binomial Coefficient

The binomial coefficient, often expressed as 'n choose k', is a mathematical tool used to determine the number of ways to select k items from a group of n items without considering the order. It is fundamental in problems of combinatorial selection where specific portions of items are chosen from groups.

Counting with Restrictions

This concept applies when there are limitations on the selection process, such as only allowing a certain maximum number of items from each group. It requires adjusting the basic combinatorial formulas to account for these constraints, ensuring that the overall count of selected items adheres to the given restrictions.

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