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Chapter 6: Problem 10

How many three-letter code words can be constructed from the first ten letters of the Greek alphabet if no repetitions are allowed?

Short Answer

Expert verified
There are 720 distinct three-letter code words that can be created from the first ten letters of the Greek alphabet with no repetitions allowed.

Step by step solution

01

Identify the number of elements in the total set.

The Greek alphabet has 24 letters, and we are given that we can only use the first ten letters for our code words. So, we have a total of 10 elements in our set.
02

Determine the number of positions to fill.

Since we need to create a three-letter code word, we have 3 positions to fill: the first letter, the second letter, and the third letter.
03

Calculate the number of possible choices for each position.

Since we cannot use any letter more than once, the number of choices for each position will change as we move forward. For the first position, all 10 letters are available, so we have 10 choices. For the second position, since we've already used one letter, we now have 9 choices. For the third position, now we've used two letters, so we have 8 choices left.
04

Calculate the total number of permutations using the multiplication rule.

The multiplication rule states that if we want to find the total number of permutations, we need to multiply the number of choices for each position. Total Permutations = (Choices for the first letter) x (Choices for the second letter) x (Choices for the third letter) Total Permutations = \(10 \times 9 \times 8 = 720\)
05

Interpret the result.

There are 720 distinct three-letter code words that can be created from the first ten letters of the Greek alphabet with no repetitions allowed.

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