Question:
The number of six digit numbers, whose all digits are odd (i.e., $1 , 3 , 5 , 7 , 9 )$, is
The number of six digit numbers, whose all digits are odd (i.e., $1 , 3 , 5 , 7 , 9 )$, is
Updated On: Jul 7, 2022
- $6^{5}$
- $5^{6}$
- $\frac{6!}{2!}$
- None of these
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The Correct Option is B
Solution and Explanation
Since six digit numbers whose all digits are odd out of only five available digits $1, 3, 5, 7, 9$ are to be formed suggests that repetition of digits is must. Hence required numbers is $5^6$.
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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