Question

Find the number of 5 letter words that can be formal from word pulse'PULSE' without repetition 

• A. 20
• B. 240
• C. 120
• D. 60

Answer 1

The Correct Option is C

To solve the problem, we need to find the number of 5-letter words that can be formed from the word "PULSE" without repeating any letters.

1. Understanding the Problem:
We are given the word "PULSE" which contains 5 distinct letters: P, U, L, S, E. We need to determine how many different 5-letter arrangements (words) can be made using each letter exactly once.

2. Recognizing the Mathematical Concept:
Since the order of letters matters and we cannot repeat any letters, this is a permutation problem. The number of possible arrangements is given by the factorial of the number of distinct items.

3. Applying the Permutation Formula:
For n distinct items, the number of possible permutations is n! (n factorial). Here, n = 5 (letters in "PULSE"), so we calculate 5!:

$ \text{Number of permutations} = 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 $

4. Verifying the Calculation:
We can also think step-by-step: 
- 1st letter: 5 possible choices 
- 2nd letter: 4 remaining choices 
- 3rd letter: 3 remaining choices 
- 4th letter: 2 remaining choices 
- 5th letter: 1 remaining choice 
Total arrangements = 5 × 4 × 3 × 2 × 1 = 120

Final Answer:
The number of 5-letter words that can be formed from "PULSE" without repetition is $\boxed{120}$.