Question:
The number of natural numbers less than $1000$ in which no two digits are repeated is
The number of natural numbers less than $1000$ in which no two digits are repeated is
Updated On: Jul 7, 2022
- $738$
- $585$
- $837$
- $720$
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The Correct Option is B
Solution and Explanation
Number of one digit natural number $= 9$
Number of two digit natural numbers with different digits $= 9 \times 8$
Number of three digit natural number with different digits $= 9 \times 8 \times 7$
Total number of natural number $
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Notes on Permutations
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