A political discussion group consists of 5 Democrats and 6 R

A political discussion group consists of 5 Democrats and 6 Republicans. Four people are selected to attend a conference.

I AM SOOOO CONFUSED!!!!

In how many ways can four people be selected from this group of eleven? Do I use the Counting Principal, Permutation Formula where order DOES matter, or the Combination formula?

In how many ways can four Republicans be selected from the six Republicans?  Do I use the Counting Principal, Permutation Formula where order DOES matter, or the Combination formula?

What is the probability that the group selected to attend the conference are all republicans?  Do I use the Counting Principal, Permutation Formula where order DOES matter, or the Combination formula?

To play the California lottery, a person has to correctly select 6 out of 51 numbers. What is the probability that one combination of six numbers will win? If it costs $1 to play and you receive $1,000,000 if you win, what is the expected value of the lottery?  Do I use the Counting Principal, Permutation Formula where order DOES matter, or the Combination formula?

Thank you!

Solution

#(a) :

11C4 = (11) ! / (4) ! = (11x10x9x8) / (4x3x2x1)

= 330 ways                 [ Answer ]

#(b ): 6C4 = (6) ! / (4) ! = (6x5x4x3) / (4x3x2x1)

         = 15 ways           [ Answer ]

#(c) : Probability of all being republicans = 15 / 330

= 1/22  

= 0.045                      [ Answer ]