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How many five digit numbers can be formed with the digits 0, 1, 2, 3 and 4 if no digit can be repeated?
- a)24
- b)60
- c)96
- d)120
- e)240
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
How many five digit numbers can be formed with the digits 0, 1, 2, 3 a...
Since order matters in this question (12340 is a different number from 42310), 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 0, 1, 2, 3 and 4 without repeating any digit.
Step 2: Write the objective equation enlisting all tasks
One thing to note in this question is that one of the digits is 0. When the 5 digits are arranged such that the first digit is 0 (for example: 01234), the result is a 4-digit number. The question specifically asks about the number of five digit numbers only. This means that after considering all the possible permutations of the given 5 digits, we need to subtract the cases in which the first digit is 0 (which makes the number effectively a 4-digit number)
Now, in the numbers where the first digit is 0, there are 4 digits left (1, 2, 3 and 4) to be arranged in 4 spaces.
So,
This is the objective equation.
Now, we know that
The number of ways in which 5 digits can be arranged in 5 spaces = 5P5
And
The number of ways in which 4 digits can be arranged in 4 spaces = 4P4
So, the objective equation becomes:
(Number of 5-digit numbers that can be formed using the digits 0, 1, 2, 3 and 4)
= 5P5 -4P4
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! = 5*4*3*2*1 = 120
And,
4P4 = 4! = 4*3*2*1 = 24
Step 4: Calculate the final answer
By putting these valuesin the objective equation, we get:
(Number of 5-digit numbers that can be formed using the digits 0, 1, 2, 3 and 4)
= 120 – 24 = 96
Looking at the answer choices, we see that Option C is correct.
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How many five digit numbers can be formed with the digits 0, 1, 2, 3 and 4 if no digit can be repeated?a)24b)60c)96d)120e)240Correct answer is option 'C'. Can you explain this answer?
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How many five digit numbers can be formed with the digits 0, 1, 2, 3 and 4 if no digit can be repeated?a)24b)60c)96d)120e)240Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about How many five digit numbers can be formed with the digits 0, 1, 2, 3 and 4 if no digit can be repeated?a)24b)60c)96d)120e)240Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many five digit numbers can be formed with the digits 0, 1, 2, 3 and 4 if no digit can be repeated?a)24b)60c)96d)120e)240Correct answer is option 'C'. Can you explain this answer?.
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