In how many distinct ways can the letters of the word SELLS be​ arranged?

To determine the number of distinct ways to arrange the letters in the word "SELLS," we need to account for the repetition of letters. 

The word "SELLS" consists of 5 letters: S, E, L, L, S. Here, S appears twice, and L appears twice.

The formula to calculate the number of distinct permutations of a word with repeating letters is:

\[
\frac{n!}{n_1! \cdot n_2! \cdot \ldots \cdot n_k!}
\]

where \( n \) is the total number of letters, and \( n_1, n_2, \ldots, n_k \) are the frequencies of the repeating letters.

For the word "SELLS":

- Total number of letters, \( n = 5 \)
- Frequency of S, \( n_1 = 2 \)
- Frequency of L, \( n_2 = 2 \)

So, the number of distinct arrangements is:

\[
\frac{5!}{2! \cdot 2!}
\]

Calculating the factorials:

\[
5! = 5 \times 4 \times 3 \times 2 \times 1 = 120
\]
\[
2! = 2 \times 1 = 2
\]

Substituting these values into the formula:

\[
\frac{120}{2 \cdot 2} = \frac{120}{4} = 30
\]

Therefore, there are 30 distinct ways to arrange the letters of the word "SELLS."

Do you want any further details or have any questions?

Here are 5 more questions you might find interesting:
1. How many distinct ways can the letters of the word "MATHEMATICS" be arranged?
2. What is the probability of drawing an ace from a standard deck of cards?
3. How do you calculate the area of a triangle given its base and height?
4. How many ways can a committee of 4 people be chosen from a group of 10?
5. What is the derivative of the function \( f(x) = x^3 + 2x^2 - 5x + 7 \)?

Tip: When dealing with permutations of letters in a word with repetitions, always remember to divide by the factorial of the frequencies of each repeated letter.

Discover how many distinct ways the letters S, E, L, L, S can be arranged using permutations with repetition. Learn the formula for calculating permutations of words with repeating letters. Suitable for students in Grades 6-8 studying combinatorics and basic permutations.

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