Problem:
Preparing a plate of cookies for 8 children, 3 types cookies {chocolate chip, peanut butter, oatmeal}, unlimited amount of cookies in supply but only cookie per child.
One cookie per plate, one plate 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
Provide complete and step by step solution for the question and show calculations and use formulas.