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

a) 30
b) 90
c) 180
d) 720

Answer: c
Explanation: The given word contains 6 letter out of which R is taken 2 times, U is taken to 2 times and other letters are all different.
∴ Required number of ways
$$\eqalign{ & = \frac{{6!}}{{2! \times 2!}} \cr & = \frac{{6 \times 5 \times 4 \times 3 \times 2 \times 1}}{{2 \times 2}} \cr & = 180 \cr} $$

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