Question:
The number of natural numbers less than $7,000$ which can be formed by using the digits $0,1,3,7,9$ (repitition of digits allowed) is equal to :
The number of natural numbers less than $7,000$ which can be formed by using the digits $0,1,3,7,9$ (repitition of digits allowed) is equal to :
Updated On: July 22, 2025
- 250
- 374
- 372
- 375
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The Correct Option is B
Solution and Explanation
Number of numbers = $2 \times 5^3$
Required number = $5^3 + 2 \times 5^3 - 1$
= 374
Required number = $5^3 + 2 \times 5^3 - 1$
= 374
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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