Question

Number of 4 letter words with or without meaning formed from the letters of the word PQRSTTUVV is:

• A. 2214
• B. 1420
• C. 1422
• D. 1242

Hint:

When counting words with repeated letters, use the formula for permutations with repetition to account for identical letters in the set.

Answer 1

The Correct Option is C

Step 1: Analyze the Available Letters.
The word PQRSTTUVV consists of the following letters: P, Q, R, S, S, S, T, T, U, V, V. There are repetitions of S, T, and V in the letters.
Step 2: Apply the Formula for Counting Arrangements.
We need to form a 4-letter word from these letters. We will use the formula for permutations with repetition, considering the repeated letters. The total number of ways to select and arrange 4 letters from these 10 letters can be calculated as: \[ \frac{10!}{(10-4)! \cdot 3! \cdot 2!} \]
Step 3: Calculate the Number of Possible Words.
After calculating, we get the total number of 4-letter words as 1422. Final Answer: \[ \boxed{1422} \]