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All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is -

1. 180
2. 175
3. 160
4. 162

Correct answer: 180

Solution

To find the total numbers where odd digits occupy even places, we first identify the even positions available and then calculate the arrangements of the odd and even digits separately, ensuring that the odd digits (1 and 3) are placed correctly. The resulting combinations yield a total of 180 valid arrangements.

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