Every one of 50 club members, can vote for any of 4 candidates.


The total number of all possible different votes is, therefore, .




    To make this result more clear, you may think this way.


You write the protocols of voting.

In the row of 50 positions, you write the first letters of the names of 4 candidates A, B, C or D, in each position.

Thus you get the "word" of the length of 50 letters, written in this 4-symbols alphabet {A,B,C,D}.


In the 1-st  position, you may have any of 4 letters;
In the 2-nd position, you may have any of 4 letters, again, independently;
In the 3-rd position, you may have any of 4 letters, again, independently;

   . . .  and so on  till 50-th position.


In this way, you get a huge set of all possible different protocols - all possible voting  results.

The problem asks about the number of all such possible protocols,
which is the number of all possible 50-letter words, written in 4-symbol alphabet {A,B,C,D}.


In this way, you get the number  ,  which is your   ANSWER