Question

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

Options

• `3/20`

• `2/5`

• `3/28`

• `5/23`

Answer 1

Letters in the word HULULULU are rearranged. The probability of all three L being together is `underlinebb(3/28)`.

Explanation:

The word HULULULU contains 4U, 3L and 1H.

Consider 3L together i.e. we have to arrange 6 units that contains 4U.

Hence number of possible arrangements

= `(6!)/(4!)`

= 6 × 5

= 30

Number of ways of arranging all letters of given word

= `(8!)/(3!4!)`

= `(8 xx 7 xx 6 xx 5)/(3 xx 2)`

= 8 × 7 × 5

Hence required probability

= `30/(8 xx 7 xx 5)`

= `6/(8 xx 7)`

= `3/28`