Solving BRIGHT Word Arrangements

The question asks for the number of distinct 3-letter arrangements that can be formed using the letters from the word "BRIGHT" without allowing any letter to be repeated.

Identifying Key Information

• The word "BRIGHT" has 6 distinct letters: B, R, I, G, H, T.
• We need to form arrangements of 3 letters.
• Repetition of letters is not allowed.

Applying the Permutation Concept

This is a permutation problem because the order of the letters matters in an arrangement. We need to find the number of permutations of 6 distinct items taken 3 at a time.

The formula for permutations is:

$ P(n, r) = \frac{n!}{(n-r)!} $

Where:

• n is the total number of items to choose from (n=6 letters in "BRIGHT").
• r is the number of items to arrange (r=3 letters).

Calculation Steps

1. Substitute the values of n and r into the formula:

   $ P(6, 3) = \frac{6!}{(6-3)!} $

2. Simplify the denominator:

   $ P(6, 3) = \frac{6!}{3!} $

3. Expand the factorials:

   $ P(6, 3) = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} $

4. Cancel out the common terms ($3!$):

   $ P(6, 3) = 6 \times 5 \times 4 $

5. Calculate the final result:

   $ P(6, 3) = 30 \times 4 = 120 $

Therefore, there are 120 distinct 3-letter arrangements that can be formed from the letters of the word "BRIGHT" without repetition.