Multiple choice

How many different four-letter words can be formed (the words need not be meaningful) using the letters of the word GREGARIOUS such that each word starts with G and ends with R?

  1. 8P2

  2. 8P2/2!.2!

  3. 8P4

  4. 8P4/2!.2!

  5. 10P2/2!.2!
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A Correct answer
Explanation

The word GREGARIOUS has 10 letters: G, R, E, G, A, R, I, O, U, S. We need a 4-letter word starting with G and ending with R. The middle two letters must be chosen from the remaining 8 letters (R, E, G, A, I, O, U, S). Since we need to pick 2 letters from 8 and arrange them, it is 8P2.

AI explanation

The word GREGARIOUS has 10 letters, and fixing G at the start and R at the end leaves 8 distinct letters for the middle two positions. The two middle positions can be filled by arranging 2 letters out of the 8 available. Using the permutation formula, this is done in 8P2 ways.

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