[180] In how many different ways can the letters of the word 'RUMOUR' be arranged?

For Competitive Exams

In how many different ways can the letters of the word 'RUMOUR' be arranged?

128

130

180

200

Explanation:

The word 'RUMOUR' has 6 letters.

In these 6 letters, 'R' occurs 2 times, 'U' occurs 2 times and rest of the letters are different.

Hence, number of ways to arrange these letters

=$\dfrac{6!}{\left(2!\right)\left(2!\right)}$

=$\dfrac{6\times5\times4\times3\times2\times1}{\left(2\times1\right)\left(2\times1\right)}$

=180

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