To solve the problem, we need to arrange the digits of the number 223355888 so that the odd digits occupy even positions. We have:
Odd digits:
3,3,5,5Even digits: 2,2,8,8,8
The number positions can be represented as:
OEOEOEOEOWhere
E indicates even positions and
O indicates odd positions.
Steps:
Arranging Odd Digits on Even Positions:
There are 4 even positions available for the odd digits
(3,3,5,5). The number of ways to arrange these with repetitions is given by:
‌Arranging Even Digits on Odd Positions:
There are 5 odd positions available for the even digits
(2,2,8,8,8). The number of ways to arrange these with repetitions is given by:
‌Calculating Total Arrangements:
By multiplying the number of ways to arrange the odd and even digits, we get the total number of 9-digit numbers that can be formed:
‌×‌=60Thus, there are 60 different ways to arrange the digits to meet the given conditions.