In a Presidential election a political party will hold prima

In a Presidential election, a political party will hold primary elections to determine its Presidential candidate, who then select a running mate as the Vice-Presidential candidate. Assume that this running mate is chosen from one of the losing candidates in the primary elections.

This is a 2 part question, with the method of how to count the lists changing slightly.

(a) If the Democratic Party has 8 primary election candidates, then how many different Democratic slates are possible? NOTE: A slate consists of a Presidential candidate and a Vice-Presidential candidate?

I am using the n k formula for binomial coeffiecients, and n=8, k=2. I got 28 which doesnt seem right? Writing them all out I got 56. Help?

(b) If we think each slate in part (a) as a team of two candidates and DO NOT consider which person is the Presidential candidate or Vice-Presidential candidate, then how many Democratic teams are possible?

Not to sure what to do here, I feel as if the answer uses n, k binomial and in that case I get either 28, or 36. Please help!

Solution

a)

The permutations for P(n,k) = n! / (n - k)!

    in this n k formula for binomial coeffiecients, and n=8, k=2.

A slate consists of a Presidential candidate and a Vice-Presidential candidate?

            =8!/(8-2)! =8*7 =56

b)the Presidential candidate or Vice-Presidential candidate,

the combinations for C(n,k) = n! / k! (n - k)!.

for n=8, k=2

    C(n,k)=8!/2!(8-2)! =4*7 =28.