Question

in how many distinct ways can the letters of the word reader be arranged?

□ ways
(type a whole number.)

Explanation:

Step1: Count the total number of letters

The word "READER" has \(6\) letters.

Step2: Count the number of repeated letters

The letter 'R' appears \(2\) times and the letter 'E' appears \(2\) times.

Step3: Use the formula for permutations of multi - set

The formula for permutations of a multi - set with \(n\) objects, where \(n_1\) of one kind, \(n_2\) of another kind, \(\cdots\), \(n_k\) of the \(k\)th kind is \(\frac{n!}{n_1!n_2!\cdots n_k!}\). Here \(n = 6\), \(n_1=2\) (for 'R') and \(n_2 = 2\) (for 'E').

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Answer:

\(180\)