Question

There are 6 multiple choice questions on an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 5 each? (a) 6000 (b) 5000 (c) 4000 (d) 8000

Name: Problem 8, Chapter 24: The Pearson Guide to Objective Arithmetic for Competitive Examinations
Uploaded: 2021-06-24T16:00:04-08:00
Duration: 1 min 8 s
Channel: James Kiss
Description: There are 6 multiple choice questions on an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 5 each? (a) 6000 (b) 5000 (c) 4000 (d) 8000

   There are 6 multiple choice questions on an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 5 each?
(a) 6000
(b) 5000
(c) 4000
(d) 8000

The Pearson Guide to Objective Arithmetic for Competitive Examinations

Dinesh Khattar 2nd Edition

Chapter 24, Problem 8

Instant Answer

Solved by Expert James Kiss

06/24/2021

Step 1

Each of these questions has 4 choices. Therefore, the total number of choices for the first three questions is calculated as follows: \[ 4 \times 4 \times 4 = 4^3 = 64 \] Show more…

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There are 6 multiple choice questions on an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 5 each? (a) 6000 (b) 5000 (c) 4000 (d) 8000

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Key Concepts

Exponentiation in Counting

When the same number of outcomes is available for several consecutive independent events, exponentiation can be used to simplify the calculation. For example, if an event with k outcomes occurs n times independently, then there are k^n possible sequences. This concept helps in efficiently calculating large products in counting problems.

Fundamental Counting Principle

This principle states that if an event can occur in m ways and another independent event can occur in n ways, then the total number of ways both events can occur is m multiplied by n. It is a key idea in combinatorics and is used to calculate the number of sequences or arrangements in a situation where each choice is independent.

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