Question

Senate committees. The u.S. Senate consists of 100 senators, 2 from each state. A committee consisting of 5 senators is to be formed.
a. How many different committees are possible?
b. How many are possible if no state may have more than 1 senator on the committee?
c. If the committee is selected at random from all 100 senators, what is the probability that no state will have both of its senators on the committee?

Answer 1

Here are your answers:

Explanation:

total ways = 100 C 5

                = 100!/ 5! (100-95)!

So 75287520 are the number of committees possible

Step 2:

Total ways = 50 c5 x (2) power 5

                  = 50!/ 5! (50-5)! x 2 power 5

                  =2118760 x 32

                  =67800320