Is LSTM a proper implementation for sequence classification

I have 20k samples in two classes namely positive and negative. Samples are formed of 10 digits and within each sample a digit is used exactly once. For instance; 0123456789 and 9876543102 are proper samples as each digit is used once. Order of the digits are what makes samples positive or negative. A classification statement for instance, positive samples can have 2 after 5, but negatives can't. Or a more intricate one like, 90% percent of positive samples have leading 0's and none of negatives have this. For the remanining 10% percent, 512 and 315 are patterns that makes samples positive.

There is a total of 10!=3.6m possible samples. So, in order to carry out a binary classification, what should be the proper ML approach? Can LSTM's handle this? Maybe a primitive Neural Network with 10 inputs and a binary classification? Or I should look for a different ML approach? Thanks.