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  4. 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?

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Q. 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?

BITSATBITSAT 2017

Solution:

$X - X - X - X - X$
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 $6 \times 10=60$.