Firstly, arrange 1,3,5,7,9 in order. Number of permutation = 1

_1_3_5_7_9_ (There are 6 spaces as shown.)

Then, put "2" in one of the 6 spaces above. Number of permutation = 6

_X_X_X_X_X_X_ (There are 7 spaces as shown.)

Then, put "4" in one of the 7 spaces above. Number of permutation = 7

_X_X_X_X_X_X_X_ (There are 8 spaces as shown.)

Then, put "6" in one of the 8 spaces above. Number of permutation = 8

_X_X_X_X_X_X_X_X_ (There are 9 spaces as shown.)

Then, put "8" in one of the 9 spaces above. Number of permutation = 9

_X_X_X_X_X_X_X_X_ (There are 10 spaces as shown.)

Lastly, put "0" in one of the 10 spaces above. Number of permutation = 10

_X_X_X_X_X_X_X_X_X_ (There are 10 spaces as shown.)

Total number of permutation

= 1 × 6 × 7 × 8 × 9 × 10

= 30240

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Special case:

If "0" is NOT allowed to put in front of the other number, number of permutation for "0" = 9

Then, total number permutation

= 1 × 6 × 7 × 8 × 9 × 9

=27216