Consider the 10 -digit number M=9876543210 . We obtain a new...

Consider the 10 -digit number $M=9876543210$. We obtain a new 10-digit number from $M$ according to the following rule: we can choose one or more disjoint pairs of adjacent digits in $M$ and interchange the digits in these chosen pairs, keeping the remaining digits in their own places. For example, from $M=9876343210$, by interchanging the 2 underlined pairs, and keeping the others in their places, we get $M_1=9786453210$. Note that any number of (disjoint) pairs can be interchanged. Find the number of new numbers that can be so obtained from $M$.