Question

What will be the ratio of number of arrangements obtained using all the letters of the word ROLLS and DOLLS?

Answer 1

In 5 letters of the word ROLLS, the letter L comes two times.

Total permutations = \(\frac{5!}{2!}=\frac{120}{2}\) = 60

In 5 letters of the word DOLLS, the letter L comes two times

Total permutations = \(\frac{5!}{2!}=\frac{120}{2}\) = 60

∴ The ratio of number of arrangements of all the letters of the word ROLLS and

DOLLS = 60 / 60 = 1 / 1 = 1 : 1