Solve the following and show all work

6. There are 8 members of the Lucky Stars Team. In how many ways can they line up for a team photo if: a) No restrictions? b) Mike and Tamara must stand beside each other? c) Tanya and Justin cannot stand next to one another? 7. Twenty-four dogs are in a kennel. Twelve of the dogs are black, six of the dogs have short tails and fteen of the dogs have long hair. There is only one dog that is black with a short tail and long hair. Two of the dogs are black with short tails. Two of the dogs have short tails and long hair. All of the dogs in the kennel have at least one the of three characteristics. a) Draw a Venn diagram to illustrate this scenario. A A" b) How many dogs are black with long hair but don't have short tails? 8. How many arrangements are there of the word PARAMETER if: a) No restrictions b) The word must start with an \"A\" and end with an \"R\" c) It must contain the word \"MEAT\