Name: Julian Sanders 1) For these short answer questions, give a short concise one or two sentence reason/argument/calculation. Avoid long detailed proofs. (p) We have a circular bracelet made of 4 equally spaced beads. What is the number of different ways to paint the beads using 5 colors? (Two colorings of the bracelet are considered the same if we can get from one bracelet to the other by some combination of rotations and flips, and in any one coloring of the bracelet you can use 1, 2, 3, or 4 of the available colors.) Concise Reason (q) Let G be a finite group of order 315 = 32 x 5 x 7, and assume that H and K are subgroups of order 15 and 21 respectively. Then can (H, K) possibly not be a normal subgroup of G? Concise Reason P207