Multiple choice

How many different words can be formed from the letters of the word GADOLINIUM, when the letter G always occupies the first place?

  1. 9!

  2. 9!/2!

  3. 10!

  4. 10C10

  5. 9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Word is GADOLINIUM (10 letters). G is fixed at start. Remaining letters: A, D, O, L, I, N, I, U, M (9 letters). I repeats twice. Permutations = 9! / 2!.

AI explanation

The word GADOLINIUM has 10 letters where the letter I is repeated twice. Fixing G in the first position leaves 9 remaining positions to be filled by the other 9 letters. Using the permutations formula for non-distinct items, the nine remaining letters can be arranged in 9 factorial divided by 2 factorial ways. The result is 9!/2!.

Keep practicing — related questions