Q81 / 150 · MHT CET 2018 · Mathematics

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

A
$\frac{3}{20}$
B
$\frac{2}{5}$
Correct answer
C
$\frac{3}{28}$
D
$\frac{5}{23}$

Solution

n (S) = \frac{8!}{4! 3!}

(total arrangements)

n (A) = \frac{6!}{4!}

(Arrangement when all L together)
So, the required probability is

P (A) = \frac{n (A)}{n (S)} = \frac{\frac{6!}{4!}}{\frac{8!}{4! 3!}} = \frac{6! \times 3!}{8!}

P (A) = \frac{6! \times 3}{8 \times 7 \times 6!} = \frac{3}{28}

Hence, the correct answer is option: 'C'.

Relevant Questions

Three numbers are chosen from 1 to 30. The probability that minimum is 10 and maximum is 26 is _______17 Apr, 2026 (E)Classical Definition of Probability
A fair die is thrown at random. Let A be the event that the number obtained on the die is a non-even prime number and B be the event that th16 Apr, 2026 (M)Classical Definition of Probability
It is known that a box of batteries contains defective pieces and a person randomly selects batteries from this box. Then the probability di13 Apr, 2026 (E)Classical Definition of Probability
Two cards are drawn at random from a standard pack of cards. Then the probability that the draw consists of exactly one face card and exactl11 Apr, 2026 (M)Classical Definition of Probability
Three numbers are chosen at random from numbers 1 to 20 . The probability that they are consecutive is05 May, 2025 (E)Classical Definition of Probability
An urn contains 6 yellow balls and black balls. When two balls are drawn at random, the probability that both are yellow is , then the value27 Apr, 2025 (E)Classical Definition of Probability