4 students are running for club president in a club with 50 members. How many different vote counts are possible, if all 50 members are required to vote?

23426 is the answer

50 x 50 x 50 x 50

that isn't right, you're saying that people can vote more than once. I'm pretty sure it means that the 50 people only have one choice.

To find the number of different vote counts possible, we need to consider the number of ways each candidate can receive votes.

Let's consider the number of votes received by each candidate individually:

Candidate 1: They can receive votes from 0 to 50 members.
Candidate 2: Once Candidate 1 receives some votes, Candidate 2 can receive votes from 0 to the remaining number of members who haven't voted yet.
Candidate 3: Once Candidate 1 and Candidate 2 receive some votes, Candidate 3 can receive votes from 0 to the remaining number of members who haven't voted yet.
Candidate 4: Once Candidates 1, 2, and 3 receive some votes, Candidate 4 can receive votes from 0 to the remaining number of members who haven't voted yet.

Based on these considerations, we can calculate the number of different vote counts:

Step 1: Calculate the number of possible vote counts for Candidate 1:
Since Candidate 1 can receive votes from 0 to 50 members, there are 51 possible vote counts for Candidate 1.

Step 2: Calculate the number of possible vote counts for Candidate 2:
Once Candidate 1 receives some votes, Candidate 2 can receive votes from 0 to the remaining number of members who haven't voted yet. So, for each possible vote count for Candidate 1, there is a different range of possible votes for Candidate 2. In this case, the range is from 0 to (50 - vote count of Candidate 1).
Therefore, for each of the 51 possible vote counts for Candidate 1, there are (50 - vote count of Candidate 1) + 1 possible vote counts for Candidate 2.

Step 3: Calculate the number of possible vote counts for Candidate 3 and Candidate 4:
Similarly, once Candidates 1 and 2 receive some votes, Candidates 3 and 4 can receive votes from 0 to the remaining number of members who haven't voted yet.
For each possible vote count for Candidates 1 and 2, there are (50 - sum of vote counts of Candidates 1 and 2) + 1 possible vote counts for Candidates 3 and 4.

Step 4: Calculate the total number of vote counts:
To determine the total number of different vote counts possible, we need to multiply the numbers we calculated in steps 1, 2, and 3 together:
Total number of vote counts = (51) × [(50 - vote count of Candidate 1) + 1] × [(50 - sum of vote counts of Candidates 1 and 2) + 1]

You can substitute the values of vote counts for Candidates 1 and 2 into the formula to find the total number of different vote counts.