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Question:
How many different nine digit numbers can be formed from the number $223355888$ by rearranging its digits so that the odd digits occupy even positions?
How many different nine digit numbers can be formed from the number $223355888$ by rearranging its digits so that the odd digits occupy even positions?
Updated On: Jun 18, 2022
- 16
- 36
- 60
- 180
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The Correct Option is C
Solution and Explanation
$X - X - X - X - X$
The four digits $3,3,5,5$ can be arranged at $(-)$ places in $\frac{4 !}{2 ! 2 !}=6$ ways.
The five digits $2,2,8,8,8$ can be arranged at $( X )$ place in $\frac{5 !}{2 ! 3 !}=10$ ways.
Total number of arrangements is $6 \times 10=60$.
The four digits $3,3,5,5$ can be arranged at $(-)$ places in $\frac{4 !}{2 ! 2 !}=6$ ways.
The five digits $2,2,8,8,8$ can be arranged at $( X )$ place in $\frac{5 !}{2 ! 3 !}=10$ ways.
Total number of arrangements is $6 \times 10=60$.
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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
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