Questions: Secret Code Word How many 3 -letter code words can be made using the letters in the word "JUSTICE" if Part: 0 / 2 Part 1 of 2 (a) Repetitions are permitted? There are 3-letter code words that can be formed.

Secret Code Word How many 3 -letter code words can be made using the letters in the word "JUSTICE" if Part: 0 / 2 Part 1 of 2 (a) Repetitions are permitted? There are 3-letter code words that can be formed.
Transcript text: Secret Code Word How many 3 -letter code words can be made using the letters in the word "JUSTICE" if Part: $0 / 2$ Part 1 of 2 (a) Repetitions are permitted? There are $\square$ 3-letter code words that can be formed.
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Solution

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Solution Steps

Step 1: Determine the Number of Unique Letters

The word "JUSTICE" consists of the letters J, U, S, T, I, C, and E. To find the number of unique letters, we count these distinct letters:

\[ \text{Number of unique letters} = 7 \]

Step 2: Calculate the Number of 3-Letter Code Words with Repetition

When repetitions are allowed, each position in the 3-letter code word can be filled by any of the 7 unique letters. Therefore, the total number of possible code words is given by:

\[ 7^3 \]

Calculating this gives:

\[ 7^3 = 343 \]

Final Answer

The number of 3-letter code words that can be formed when repetitions are permitted is \(\boxed{343}\).

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