Question

There are six multiple choice questions in an examination. How many sequences of answers are possible, if the first two questions have 3 choices each, the next two have 4 choices each and the last two have 5 choices each? (a) 3450 (b) 3300 (c) 3600 (d) 3400

Name: Problem 9, Chapter 24: The Pearson Guide to Objective Arithmetic for Competitive Examinations
Uploaded: 2021-07-12T15:45:36-08:00
Duration: 1 min 7 s
Channel: Aman Gupta
Description: There are six multiple choice questions in an examination. How many sequences of answers are possible, if the first two questions have 3 choices each, the next two have 4 choices each and the last two have 5 choices each? (a) 3450 (b) 3300 (c) 3600 (d) 3400

   There are six multiple choice questions in an examination. How many sequences of answers are possible, if the first two questions have 3 choices each, the next two have 4 choices each and the last two have 5 choices each?
(a) 3450
(b) 3300
(c) 3600
(d) 3400

The Pearson Guide to Objective Arithmetic for Competitive Examinations

Dinesh Khattar 2nd Edition

Chapter 24, Problem 9

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Solved by Expert Aman Gupta

07/12/2021

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There are six multiple choice questions in an examination. How many sequences of answers are possible, if the first two questions have 3 choices each, the next two have 4 choices each and the last two have 5 choices each? (a) 3450 (b) 3300 (c) 3600 (d) 3400

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Key Concepts

Fundamental Counting Principle

The fundamental counting principle asserts that if there are a number of independent choices or events, the total number of outcomes is the product of the number of outcomes for each event. This principle is foundational in combinatorics and provides the basis for counting the number of possible sequences when each element in the sequence has a fixed set of options.

Independent Choice Sequences

When constructing a sequence where each element is determined by an independent choice, the total number of sequences is calculated by multiplying the number of choices available at each step. This concept is commonly applied in problems involving multiple-stage experiments, such as answering a series of multiple-choice questions, where the overall number of possible results is a product of the counts for each individual stage.

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