Question

There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same state. b How many ways can we choose a Senator from a chosen state? c How many ways can the 3-Senator committee be formed such that no two Senators are from the same state?

Answer 1

a) rCn = 1176

b) 2352

Explanation:

a)Each committee should be formed with 3 members ( no two members could be of the same state) then

Let´s fix a senator for any of the 50 states so in the new condition we need to combined 49 senators in groups of 2 then

rCn = n! / (n - r )! *r!

rCn = 49!/ (49 - 2)!*2!

rCn = 49*48*47! / 47!*2!

rCn = 49*48 /2

rCn = 1176

So we can choose in 1176 different ways a senator for a given state

b) To answer this question we have to note, that, 1176 is the number of ways a committee can be formed with senators of different sate (taking just one senator for state ) if we have 2 senators we need to multiply that figure by 2.

1176*2 = 2352