The table shows the places where the odd digits can be placed
There are 4 places
And 3 odd digits out of which 2 are of the same kind
Choose any 3 places out of the four places in 4C3 ways = 4 ways
In each way, the 3 digits can be placed in \(\frac{3!}{2!}\) ways = 3 ways
⇒ Total number of ways in which odd digits occupy odd places = 4 x 3 = 12
Now there are 4 remaining digits out of which 2 are same of 1 kind, and 2 are same as another kind
⇒ They can be arranged in the remaining places in = \(\frac{4!}{2!2!}\) = 6 ways
⇒ Total number of numbers where odd digit occupies odd places = 12 x 6 = 72
There are 72 such numbers
