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How many five digit numbers can be formed with the digits 1, 2, 3, 4 and 5 if no digit can be repeated?
- a)10
- b)50
- c)60
- d)120
- e)720
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
How many five digit numbers can be formed with the digits 1, 2, 3, 4 a...
Since order matters in this question (12345 is a different number from 42531), we can solve it using either the Filling Spaces method or the Permutation formula.
Step 1: Understand the objective
The objective of the question here is to find the number of 5-digit numbers that can be formed using the digits 1, 2, 3, 4 and 5 without repeating any digit.
Step 2: Write the objective equation enlisting all tasks
We will solve this question using the Permutation formula.
So, in this step, we will define the single task required to achieve the objective as: arranging 5 digits in 5 spaces
So, the objective equation can be written as:
(Number of 5 digit numbers that can be formed with the digits 1, 2, 3, 4 and 5)
= (Number of ways of arranging 5 digits in 5 spaces) = 5P5
Step 3: Determine the number of ways of doing each task
In Step 3, using the Permutation Formula (nPn = n!), we get that
5P5 = 5!
Now,
5! = 5*4*3*2*1 = 120
So, 5P5 = 120
Step 4: Calculate the final answer
By putting the value of 5P5 in the objective equation, we get:
(Number of 5 digit numbers that can be formed with the digits 1, 2, 3, 4 and 5) = 120
Looking at the answer choices, we see that Option D is correct.
Most Upvoted Answer
How many five digit numbers can be formed with the digits 1, 2, 3, 4 a...
Understanding the Problem
To find out how many five-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 without repeating any digits, we need to consider the arrangement of these digits.
Choosing Digits
- We have 5 unique digits: 1, 2, 3, 4, 5.
- Since we want to create a five-digit number, we will use all 5 digits.
Arranging the Digits
- The number of ways to arrange n distinct objects is given by n factorial (n!).
- In this case, n = 5 (the number of digits).
Calculating Factorial
- 5! (5 factorial) = 5 × 4 × 3 × 2 × 1
- Performing the calculation:
- 5 × 4 = 20
- 20 × 3 = 60
- 60 × 2 = 120
- 120 × 1 = 120
Final Count of Five-Digit Numbers
- Therefore, the total number of distinct five-digit numbers that can be formed using the digits 1, 2, 3, 4, and 5 without repetition is 120.
Conclusion
- The correct answer is option 'D', which corresponds to 120 different five-digit numbers.
To find out how many five-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 without repeating any digits, we need to consider the arrangement of these digits.
Choosing Digits
- We have 5 unique digits: 1, 2, 3, 4, 5.
- Since we want to create a five-digit number, we will use all 5 digits.
Arranging the Digits
- The number of ways to arrange n distinct objects is given by n factorial (n!).
- In this case, n = 5 (the number of digits).
Calculating Factorial
- 5! (5 factorial) = 5 × 4 × 3 × 2 × 1
- Performing the calculation:
- 5 × 4 = 20
- 20 × 3 = 60
- 60 × 2 = 120
- 120 × 1 = 120
Final Count of Five-Digit Numbers
- Therefore, the total number of distinct five-digit numbers that can be formed using the digits 1, 2, 3, 4, and 5 without repetition is 120.
Conclusion
- The correct answer is option 'D', which corresponds to 120 different five-digit numbers.
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Community Answer
How many five digit numbers can be formed with the digits 1, 2, 3, 4 a...
5!=5*4*3*2*1=120.
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How many five digit numbers can be formed with the digits 1, 2, 3, 4 and 5 if no digit can be repeated?a)10b)50c)60d)120e)720Correct answer is option 'D'. Can you explain this answer?
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