Question

The letters of the word "ATTRACTION' are written randomly. The probability that no two T's appear together is

Options

• `1/15`

• `4/15`

• `7/15`

• `11/15`

Answer 1

`7/15`

Explanation:

Total words = `(10!)/(2!3!)`

Number of words two T's appear together = `(9!)/(2!) - (8!)/(2!) = (8.8!)/(2!)`

Number of words no two T's appear together = `(10!)/(2!3!) - (8.8!)/(2!) = (21.8!)/(3!)`

Probability = `(21.8!.2!3!)/(3!.10!) = 7/15`