You are an amazingly successful hotelier; one of your properties is "Chez Four-Thirteen". Suppose there are 8 distinguishable hotel rooms (numbered 101, 102,...,108), each with maximum occupancy of 4 people. A bus comes in with anywhere from 1 to 32 (distinguishable) people, but you do not know exactly how many. While waiting, you decide to calculate (making use of combinatorics) the number of possible ways the people on the bus can spend the night in those hotel rooms so you can make a welcome sign. Determine this number. Use a computer to express the answer with all the digits (e.g., 31415926535897932384626433832795); write down for your check-in clerk the order of magnitude (e.g., 10³²). I recommend python to do the computation.