Statistics Through Applications
Statistics Through Applications
2nd Edition
ISBN: 9781429219747
Author: Daren S. Starnes, David Moore, Dan Yates
Publisher: Macmillan Higher Education
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Chapter 8.2, Problem 8.40E

(a)

To determine

To calculate how many four letter call signs start with the letter W.

(a)

Expert Solution
Check Mark

Answer to Problem 8.40E

  17576 signs.

Explanation of Solution

Use the multiplication principle and that there are 26 letters:

  1×26×26×26=17576

(b)

To determine

To calculate how many four letter call signs start with the letter W are possible with the restrictions given.

(b)

Expert Solution
Check Mark

Answer to Problem 8.40E

There are 17525 possibilities with the restrictions.

Explanation of Solution

Determine the number of signs from (a) that have three repeating letters using multiplication counting principle:

Not the first letter: 1×25×1×1=25

First letter: 1×26×1×1=26

Thus in total there are 51 possibilities that have three or more repeated letters.

  1757651=17525

Thus there are 17525 possibilities with the restrictions.

(c)

To determine

To calculate how many four letter call signs start with the letter W or K and meet the restrictions in (b).

(c)

Expert Solution
Check Mark

Answer to Problem 8.40E

There are 35050 possibilities with the restrictions.

Explanation of Solution

Use the multiplication principle and that there are 26 letters:

  2×26×26×26=35152

Determine the number of signs from (a) that have three repeating letters using multiplication counting principle:

Not the first letter: 2×25×1×1=50

First letter: 2×26×1×1=52

Thus in total there are 102 possibilities that have three or more repeated letters.

  35152102=35050

Thus there are 35050 possibilities with the restrictions.

Chapter 8 Solutions

Statistics Through Applications

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