I have a group of 10 people. 6 are for hot dogs, 4 against. I make

a new group of 5 people from my first group of 10, 1 person for hot dogs and the other 4 randomly selected from the remaining 9 members of the original group – what is the formula to calculate the probability that all the members of my new group will be for hot dogs, that a majority of my new group will be for hot dogs, and that 4 to 1 members of my new group will be for hot dogs? Assume no members change their minds about being for or against hot dogs.