Problem 1. Cutting Substrings (4 Points) For this problem, we will look at strings of n distinguishable beads, of this form (assume n> 100): 3 n a) Using scissors, we will cut the string in 10 different locations. How many ways are there to reorder the pieces, assuming we do not rotate them at all, and we only perform a single cut between each pair of beads? b) Assume now we are allowed to rotate the pieces, and we are able to differentiate the direction of each bead (the strings depicted below are different): How many ways are there to reorder the pieces, still making 10 cuts? c) This time we will perform only one cut with the scissors, and we cannot differentiate rotations of a single bead, however strings of heads can be rotated and are differen- tialable. How many ways are there to cut and reorder the string pieces? To illustrate, these will be considered the same string: and these would be considered diferent strings Problem 1. Cutting Substrings (4 Points) For this problem, we will look at strings of n distinguishable beads, of this form (assume n> 100): 3 n a) Using scissors, we will cut the string in 10 different locations. How many ways are there to reorder the pieces, assuming we do not rotate them at all, and we only perform a single cut between each pair of beads? b) Assume now we are allowed to rotate the pieces, and we are able to differentiate the direction of each bead (the strings depicted below are different): How many ways are there to reorder the pieces, still making 10 cuts? c) This time we will perform only one cut with the scissors, and we cannot differentiate rotations of a single bead, however strings of heads can be rotated and are differen- tialable. How many ways are there to cut and reorder the string pieces? To illustrate, these will be considered the same string: and these would be considered diferent strings