Multiple choice

The letter of the word $'FORTUNATES'$ are arranged randomly in a row. What is the chance that the two $'T'$ come together.

  1. $\dfrac {1}{6}$
  2. <ul><li>$\dfrac {1}{7}$</li></ul>
  3. $\dfrac {1}{3}$
  4. $\dfrac {1}{5}$
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D Correct answer
Explanation

Word 'FORTUNATES' has 10 letters: F, O, R, T, U, N, A, T, E, S. Two T's. Total arrangements = 10!/2!. Arrangements with T's together = treat TT as one unit, so 9! arrangements. Probability = 9! / (10!/2!) = 2 * 9! / 10! = 2/10 = 1/5.

AI explanation

The word FORTUNATES contains 10 letters including 2 identical T's, making the total number of arrangements 10! / 2!. To find the probability of the two T's coming together, treat them as a single combined letter, giving 9! favorable arrangements. The probability is 9! divided by (10! / 2!), which simplifies to (2 * 9!) / 10! = 2 / 10 = 1 / 5.

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