Prove the statements that are true and give counterexample to disprove those that are false

Prove the statements that are true and give counterexample to disprove those that are false. For all integers n, if n is prime then (-1)^n=-1 (READ:...then (-1) to the n power equal -1)

Using Permutations and Combinations

How many distinct nonnegative integer solutions are there to the equation x1 + x2 + x3 =7 in which x1 is greater than or equal to 3.

Using Permutations and Combinations

Can you check my answers and help me with B ? thank you. Preparing a plate of cookies for children, 3 cookies {chocolate chip, peanut butter, oatmeal} - one cookie per child A) How many different plates can be prepared? C(8,3) = 56 B) How many different plates can be prepared if at least one of each kind of cookie is given out ? C) How many different plates can be prepared if no one likes oatmeal? C(8,2) = 28 D) How many different plates can be prepared if two children need to get peanut butter? C(6,3) = + C(2,1) = 22 E) How many different plates can be prepared if the dog got into the kitchen and three are only two chocolate chip cookies left? C(6,2) + 2 = 17