Multiple choice

In how many ways can the letters of the word GARGANTUNG be rearranged such that all the G’s appear together?

  1. 8!/ 3!2!2!

  2. 8!/2!2!

  3. 8! .3!/2!2!

  4. 8!/2!.3!

  5. 10!/3!.2!.2!
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

GARGANTUNG has 10 letters: G(3), A(2), R(1), N(2), T(1), U(1). Treating the three G's as one block, we arrange 8 items (the block + 7 remaining letters). The remaining letters are A(2), R(1), N(2), T(1), U(1). Total arrangements = 8! / (2! * 2!).

AI explanation

The word GARGANTUNG has 10 letters, with 3 G letters, 2 A letters, and 2 N letters. Grouping the 3 G letters together into a single unit reduces the total items to arrange to 8. Because the A and N letters are repeated, the number of arrangements is 8! divided by the product of 2! and 2!.

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