Why the reversed logic? Why can't it be answered with C(10, 4) = 210? Answer to Problem 40EThe number of four-letter words (including nonsense words) using four different letters from A through Jis210.Explanation of SolutionGiven information:The alphabets from A to J.Formula used:The bionomial theorem C (n,r) =Calculation:To obtain four-letter words (including nonsense words) using four different letters form A through J can bestring as ABCDEFGHIJ and remove six alphabet. This sample is just an unordered selection of 6 digits out of10. We are concerned here with combinations. Since the six digits can be selected in selected in C (10, 6)ways. Numerically we haveC(10,6)==10!6!(10-6)!10!6!.4!n!r!(n-r)! *10.9.8.7.6.56.5.4.3.2.1= 210Therefore, the number of four-letter words (including nonsense words) using four different letters from Athrough Jis 210.

It is given that we have to choose four different letters from A to J to obtain the four-letter…

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The number of four-letter words (including nonsense words) using four different letters from A through Jis 210.

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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Question

Why the reversed logic? Why can't it be answered with C(10, 4) = 210?

Answer to Problem 40E
The number of four-letter words (including nonsense words) using four different letters from A through Jis
210.
Explanation of Solution
Given information:
The alphabets from A to J.
Formula used:
The bionomial theorem C (n,r) =
Calculation:
To obtain four-letter words (including nonsense words) using four different letters form A through J can be
string as ABCDEFGHIJ and remove six alphabet. This sample is just an unordered selection of 6 digits out of
10. We are concerned here with combinations. Since the six digits can be selected in selected in C (10, 6)
ways. Numerically we have
C(10,6)
=
=
10!
6!(10-6)!
10!
6!.4!
n!
r!(n-r)! *
10.9.8.7.6.5
6.5.4.3.2.1
= 210
Therefore, the number of four-letter words (including nonsense words) using four different letters from A
through Jis 210.

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