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🗣 Wd提问: dns edge

🤖 Ai回答:
To solve the problem, we need to determine the number of distinct permutations of the letters in the word dns edge、The word dns edge consists of the letters d, n, s, e, d, g, e, which include repeated letters、Specifically, the letter d appears twice and the letter e appears twice.

The formula for the number of distinct permutations of a word with repeated letters is given by:

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

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

For the word dns edge:
The total number of letters \( n \) is 7.
The frequency of the letter d, \( n_1 \), is 2.
The frequency of the letter n, \( n_2 \), is 1.
The frequency of the letter s, \( n_3 \), is 1.
The frequency of the letter e, \( n_4 \), is 2.
The frequency of the letter g, \( n_5 \), is 1.
The frequency of the letter a, \( n_6 \), is 1.

Substituting these values into the formula, we get:

\[
\frac{7!}{2! \cdot 2!}
\]

First, we calculate \( 7! \):

\[
7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040
\]

Next, we calculate \( 2! \):

\[
2! = 2 \times 1 = 2
\]

So, the expression becomes:

\[
\frac{5040}{2 \times 2} = \frac{5040}{4} = 1260
\]

Therefore, the number of distinct permutations of the letters in the word dns edge is \(\boxed{1260}\).

Ai作答

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