Chapter 9.1, Problem 8E

Solution

To state: The numbers of 3-letter crossword puzzle entries that can be formed excluding letter J, Q, X, and Z without repeating the letters.

The resultant answer is 9240 ways.

Given information:

3-letter crossword puzzle entries are to be formed excluding letter J, Q, X, and Z without repeating the letters.

Explanation:

Number of letters is: 26

Remaining letters after excluding letters J, Q, X, and Z: $26-4=22$

3-letter crossword puzzle entries need to be formed that means 3 places have to be filled.

Any of the 22 letters can be placed at the first place. Thus there are 22 ways in which the first letter can be filled.

Now 21 letters are remaining, the second place can be filled with any of the 21 letters.

Now 20 letters are remaining, the third place can be filled with any of the 20 letters.

The number of words is:

  $22\cdot 21\cdot 20=9240$

Therefore, there are 9240 ways in which 3-letter crossword puzzle entries can be formed.