I need a little help with this problem:-
A committee is formed consisting of one representative from each of the 50 states in the United States, where the representative from a state is either the governor or one of the two senators from that state. How many ways are there to form this committee?
I tried using the formula but am not getting the correct answer.
Dear sllcapri21,
Correct. Now there are 50 states is'nt?? So for the first state we could assign one of the three members. Similarly for the second, third, forth, fifth,...........and fiftieth. So using the "Basic principle of counting" can you give me an idea about the ways in which the commitee could be formed.
Dear sllcapri21,
Well thats an idea...But do you know about the "Basic principle of counting"?? If you don't please refer http://en.wikipedia.org/wiki/Rule_of_product.(Just read the first few paragraphs)
Dear sllcapri,
Possibly you are confused by the complexity of the definition. But if I explain it simply, it means that if you have two events which could be done in and ways respectively,the total number of ways both events could be done is .
Example:Suppose you toss a coin and a dice,
Number of outcomes from the coin=2
Number of outcomes from the dice=6
Therefore from the "Basic principle of counting",
Number of total outcomes=
Did you get the idea??
You could write the sample space and verify...
S={Heads and 1,Heads and 2,Heads and 3,Heads and 4,Heads and 5,Heads and 6,Tails and 1,Tails and 2,Tails and 3,Tails and 4,Tails and 5,Tails and 6}