A political discussion group consists of 5 Democrats and 6 Republicans. Four peo
ID: 3029844 • Letter: A
Question
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!
Explanation / Answer
#(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 ]