You are given a pack of 13 playing cards. A possible shuffling algorithm is to cut or divide the pack into three parts, A, B, and C, and assemble the parts into a new order, different from ABC. This process can then be repeated as many times as are needed to obtain a sufficiently shuffled pack. (a) In how many ways can the pack be cut into three, assuming that each part has at least one card? Show your working.
(b) In how many ways can the three parts be reassembled, other than in the order ABC? Give a numeric result, as well as the method by which you obtain the result. Verify the result by enumerating the possible orders.

Question

You are given a pack of 13 playing cards. A possible shuffling algorithm is to cut or divide the pack into three parts, A, B, and C, and assemble the parts into a new order, different from ABC.  This process can then be repeated as many times as are needed to obtain a sufficiently shuffled pack. (a)  In how many ways can the pack be cut into three, assuming that each part has at least one card? Show your working.
(b)  In how many ways can the three parts be reassembled, other than in the order ABC? Give a numeric result, as well as the method by which you obtain the result. Verify the result by enumerating the possible orders.