I don't understand my professor's explanation for this problem, please help!
A flea is sitting on the grass near 5 dogs: A, B, C, D, and E. The flea jumps onto 1 of the dogs and proceeds to jump from dog to dog, biting each dog one time. The flea bites exactly 1 of the dogs exactly twice however the flea does NOT jump on the SAME dog twice in a row. In how many ways can the flea bite the dogs?
Explanation: 5 choices for the twice bitten dog, 10 jump patterns, and 4! ways of biting the other dogs. total: 10 x 5! = 1200.
I just don't understand how you get 10 jump patterns. Shouldn't it be 4!?
And why would this 1 have only 5 jump patterns: The flea now makes consecutive jumps (that is jumps twice in a row) on the dog that will be bitten twice. In how many ways can the flea bite the dogs? 5 choices for the twice bitten dog. 5 jump patterns and 4! ways of biting the other dogs. Thanks!