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  4. Letters in the word HULULULU are rearranged. The probability of all three L being together is

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Q. Letters in the word HULULULU are rearranged. The probability of all three L being together is

MHT CETMHT CET 2018

Solution:

Given words, HULULULU
$\therefore $ Total number of sample space $=\frac{8 !}{4 ! 3 !}$
and total number of ways all three $L$ being together $=\frac{6 !}{41}$
Required probability $=\frac{\frac{6 !}{4!}}{\frac{8 !}{4 ! 3 !}}$
$=\frac{6! \times 3!}{8 !}=\frac{3}{28}$