Question:
The number of numbers between $2,000$ and $5,000$ that can be formed with the digits $0, 1, 2, 3, 4$ (repetition of digits is not allowed) and are multiple of $3$ is :
The number of numbers between $2,000$ and $5,000$ that can be formed with the digits $0, 1, 2, 3, 4$ (repetition of digits is not allowed) and are multiple of $3$ is :
Updated On: Feb 14, 2025
- 24
- 30
- 36
- 48
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The Correct Option is B
Solution and Explanation
Number between 2,000 and 5,000 is 4 digits number.
Using $0,1,2,3,4$ (repetition of digits is not allowed) and are multiple of 3 .
For multiple of 3 , the sum of all digits should be divisible by $3 $
So, number can be formed $0,1,2,3$ (sum is 6 which is divisible by 3) or $0,2,3,4$ (sum is 9 which is divisible 1 cannot be on highest digit in the number.
Therefore, number of 4 digit numbers $=2 \times 3 !+3 \times 3 !=30$
Using $0,1,2,3,4$ (repetition of digits is not allowed) and are multiple of 3 .
For multiple of 3 , the sum of all digits should be divisible by $3 $
So, number can be formed $0,1,2,3$ (sum is 6 which is divisible by 3) or $0,2,3,4$ (sum is 9 which is divisible 1 cannot be on highest digit in the number.
Therefore, number of 4 digit numbers $=2 \times 3 !+3 \times 3 !=30$
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Concepts Used:
Permutations
A permutation is an arrangement of multiple objects in a particular order taken a few or all at a time. The formula for permutation is as follows:
\(^nP_r = \frac{n!}{(n-r)!}\)
nPr = permutation
n = total number of objects
r = number of objects selected
Types of Permutation
- Permutation of n different things where repeating is not allowed
- Permutation of n different things where repeating is allowed
- Permutation of similar kinds or duplicate objects